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HTML 

              
                <div
  class="carousel"
  role="region"
  aria-label="gallery"
  x-data="carousel"
>
  <div class="relative">
    <!-- controls -->
    <ul aria-label="gallery controls" role="list">	
      <li>
        <button class="arrow arrow--prev" @click="go('prev')">
          <div class="sr-only">Previous</div>
          <svg height="13" width="13" aria-hidden="true" fill="none" viewBox="0 0 6 10" xmlns="http://www.w3.org/2000/svg"><path d="M5 9.4.6 5 5 .6" stroke="currentColor" stroke-width="1.2" stroke-linecap="round" stroke-linejoin="round"/></svg>
        </button>
      </li>
      <li>
        <button class="arrow arrow--next" @click="go('next')">
          <div class="sr-only">Next</div>
          <svg height="13" width="13" aria-hidden="true" fill="none" viewBox="0 0 6 10" xmlns="http://www.w3.org/2000/svg"><path d="M1 .6 5.4 5 1 9.4" stroke="currentColor" stroke-width="1.2" stroke-linecap="round" stroke-linejoin="round"/></svg>
        </button>
      </li>
    </ul>

    <!-- carousel scroller -->
    <ul
        class="carousel__scroll"
        :class="{
          'carousel__scroll--active': momentum.active,
          'carousel__scroll--dragging': momentum.dragging
        }"
        role="list"
        tabindex="0"
        aria-label="gallery images"
    >
      <li class="carousel__slide">
        <img class="image" src="https://source.unsplash.com/ePpaQC2c1xA/700x700/" width="700" height="700" alt="" loading="lazy" decoding="async">
      </li>
      <li class="carousel__slide">
        <img class="image" src="https://source.unsplash.com/phIFdC6lA4E/700x700/" width="700" height="700" alt="" loading="lazy" decoding="async">
      </li>
      <li class="carousel__slide">
        <img class="image" src="https://source.unsplash.com/9wg5jCEPBsw/700x700/" width="700" height="700" alt="" loading="lazy" decoding="async">
      </li>
      <li class="carousel__slide">
        <img class="image" src="https://source.unsplash.com/g30P1zcOzXo/700x700/" width="700" height="700" alt="" loading="lazy" decoding="async">
      </li>
      <li class="carousel__slide">
        <img class="image" src="https://source.unsplash.com/73F4pKoUkM0/700x700/" width="700" height="700" alt="" loading="lazy" decoding="async">
      </li>
    </ul>
  </div>

  <ul class="pagination" role="list" aria-label="pagination">
    <li>
      <button
        class="pagination__item"
        @click="go(0)"
        :aria-pressed="(index === 0).toString()"
      >
        <div class="sr-only">go to page 1 of 1</div>
        <img src="https://source.unsplash.com/ePpaQC2c1xA/40x40/" width="40" height="40" alt="" loading="lazy" decoding="async">
      </button>
    </li>
    <li>
      <button
        class="pagination__item"
        @click="go(1)"
        :aria-pressed="(index === 1).toString()"
      >
        <div class="sr-only">go to slide 2 of 5</div>
        <img src="https://source.unsplash.com/phIFdC6lA4E/40x40/" width="40" height="40" alt="" loading="lazy" decoding="async">
      </button>
    </li>
    <li>
      <button
        class="pagination__item"
        @click="go(2)"
        :aria-pressed="(index === 2).toString()"
      >
        <div class="sr-only">go to slide 3 of 5</div>
        <img src="https://source.unsplash.com/9wg5jCEPBsw/40x40/" width="40" height="40" alt="" loading="lazy" decoding="async">
      </button>
    </li>
    <li>
      <button
        class="pagination__item"
        @click="go(3)"
        :aria-pressed="(index === 3).toString()"
      >
        <div class="sr-only">go to slide 4 of 5</div>
        <img src="https://source.unsplash.com/g30P1zcOzXo/40x40/" width="40" height="40" alt="" loading="lazy" decoding="async">
      </button>
    </li>
    <li>
      <button
        class="pagination__item"
        @click="go(4)"
        :aria-pressed="(index === 4).toString()"
      >
        <div class="sr-only">go to slide 5 of 5</div>
        <img src="https://source.unsplash.com/73F4pKoUkM0/40x40/" width="40" height="40" alt="" loading="lazy" decoding="async">
      </button>
    </li>
  </ul>
</div>
!

CSS 

              
                .carousel {
  position: relative;
  
  &__scroll {
    display: flex;
    gap: 1rem;
    overflow: auto;
		cursor: grab;
		-webkit-overflow-scrolling: touch;
		scroll-snap-type: x mandatory;
		scroll-behavior: smooth;
		user-select: none;
    background: #f8f8f8;

		&--active {
			scroll-snap-type: unset;
			scroll-behavior: unset;
		}

		&--dragging {
			cursor: grabbing;
		}

		// hide scrollbars
		scrollbar-width: none;

		&::-webkit-scrollbar {
			display: none;
		}
  }
  
  &__slide {
		scroll-snap-align: center;
    width: 100%;
    flex-shrink: 0;
  }
}

.arrow {
  position: absolute;
  top: calc(50% - 1rem);
  
  display: flex;
  justify-content: center;
  align-items: center;
  
  width: 2rem;
  height: 2rem;
  
  border-radius: 1rem;
  background: rgb(154, 63, 32);
  color: #fff;
  
  &--prev {
    left: -1rem;
  }
  
  &--next {
    right: -1rem;
  }
}

.pagination {
  display: flex;
  justify-content: center;
  align-items: center;
  gap: .5rem;
  margin-top: 1rem;
  
  &__item {
    padding: .5rem;
    border: 1px solid transparent;
    transition: border-color .2s;
    
    &[aria-pressed="true"] {
      border-color: #000;
    }
  }
}

/**
 * misc
 */
.sr-only {
  position: absolute;
  width: 1px;
  height: 1px;
  padding: 0;
  margin: -1px;
  overflow: hidden;
  clip: rect(0, 0, 0, 0);
  white-space: nowrap;
  border-width: 0;
}

.relative {
  position: relative;
}

ul {
  list-style-type: none;
  margin: 0;
  padding: 0;
}

body {
  max-width: 30rem;
  padding: 2rem;
  margin: 0 auto;
  font-family: system-ui;
}

img {
  display: block;
  width: 100%;
  height: auto;
}

button {
  appearance: none;
  cursor: pointer;
  border: 0;
  padding: 0;
}
!

JS 

              
                import Alpine from "https://cdn.skypack.dev/[email protected]";

Alpine.data('carousel', function carousel() {
	return {
		scrollEl: null,

		index: 0,

		momentum: {
			active: false,
			handler: null,
			dragging: false,
			velocity: 0,
			startPos: 0,
			scrollLeft: 0,
		},

		init() {
			this.scrollEl = this.$root.querySelector(".carousel__scroll");

			this.dragScroll();
			this.updateIndex();
		},

		// move the slider
		go(mode) {
			this.scrollEl.scrollLeft = this.getNewPos(mode);
		},

		// get the new position of the slider after movement
		getNewPos(mode) {
			const currentScroll = this.scrollEl.scrollLeft;
			const slideWidth = this.scrollEl.offsetWidth;
			const scrollWidth = this.scrollEl.scrollWidth;

			let newScrollPos = currentScroll;

			// next
			if (mode === "next") {
				newScrollPos += slideWidth;
				// we're within 20px of the end so loop to the start
				if (Math.abs(scrollWidth - newScrollPos) < 20) {
					newScrollPos = 0;
				}
				return newScrollPos;
			}

			// prev
			if (mode === "prev") {
				// we're within 20px of the beginning so loop to the end
				if (Math.abs(newScrollPos) < 20) {
					return scrollWidth - slideWidth;
				}
				return (newScrollPos -= slideWidth);
			}

			// an index
			const index = parseInt(mode);
			if (typeof index === "number") {
				return (newScrollPos = slideWidth * index);
			}
		},

		/**
		 * update index
		 */
		updateIndex() {
			const slides = [...this.$root.querySelectorAll(".carousel__slide")];

			const observer = new IntersectionObserver(
				(entries, observer) => {
					// get the state of what slides are visible
					const state = [];
					for (const entry of entries) {
						const index = slides.indexOf(entry.target);
						state[index] = entry.intersectionRatio > 0.5;
					}

					// set index to the first visible slide
					const index = state.findIndex((v) => v);
					if (index !== -1) this.index = index;
				},
				{
					root: this.scrollEl,
					threshold: 0.5,
				}
			);

			for (const slide of slides) {
				observer.observe(slide);
			}
		},

		/**
		 * momentum drag for mouse users
		 */
		dragScroll() {
			this.scrollEl.addEventListener("mousedown", (e) => {
				this.momentum.dragging = true;
				this.momentum.active = true;
				this.momentum.startPos = e.pageX - this.scrollEl.offsetLeft;
				this.momentum.scrollLeft = this.scrollEl.scrollLeft;

				this.cancelMomentum();
			});

			this.scrollEl.addEventListener("mouseup", () => {
				this.momentum.dragging = false;
				this.beginMomentum();
			});

			this.scrollEl.addEventListener("mouseleave", () => {
				this.momentum.dragging = false;
				this.beginMomentum();
			});

			this.scrollEl.addEventListener("mousemove", (e) => {
				if (!this.momentum.dragging) return;
				e.preventDefault();

				const x = e.pageX - this.scrollEl.offsetLeft;
				const walk = x - this.momentum.startPos;

				// store the previous scroll position
				const prevScrollLeft = this.scrollEl.scrollLeft;
				this.scrollEl.scrollLeft = this.momentum.scrollLeft - walk;

				// Compare change in position to work out drag speed
				this.momentum.velocity = this.scrollEl.scrollLeft - prevScrollLeft;
			});

			this.scrollEl.addEventListener("wheel", (e) => {
				this.cancelMomentum();
			});
      
      const images = this.scrollEl.querySelectorAll('img')
      for (let image of images) {
        image.addEventListener('dragstart', e => e.preventDefault())
      }
		},

		beginMomentum() {
			this.cancelMomentum();
			this.momentum.handler = requestAnimationFrame(() => this.momentumLoop());
		},

		cancelMomentum() {
			cancelAnimationFrame(this.momentum.handler);
		},

		momentumLoop() {
			this.scrollEl.scrollLeft += this.momentum.velocity;
			this.momentum.velocity *= 0.95; // slow the velocity slightly
			// are we still moving?
			if (Math.abs(this.momentum.velocity) > 0.5) {
				this.momentum.handler = requestAnimationFrame(() =>
					this.momentumLoop()
				);
			} else {
				this.momentum.active = false;
			}
		},
	};
})

Alpine.start()
!
999px

Console