Very simplified version of nested dropdown tracking.

dropdown.svelte

<!-- This is missing a bunch of the code that interacts with tippy to position the element, but
 hopefully it makes sense -->
<script>
  // The popup tracker makes sure that "outside click" handling doesn't trigger when a click occurs
  // in a child dropdown, and the child dropdown's popup is fixed.
  function makePopupTracker(parent) {
    let contained: HTMLElement[] = [];
    return {
      contains(target) {
        return contained.some((e) => e.contains(target));
      },
      register(element: HTMLElement) {
        if (parent) {
          parent.register(element);
        }

        contained.push(element);
      },
      unregister(element: HTMLElement) {
        if (parent) {
          parent.unregister(element);
        }
        contained = contained.filter((e) => e !== element);
      },
    };
  }

  // Get the popup tracker from the parent context, if any,
  // and create a new popup tracker that inherits it.
  let parentTracker = getContext('parent-dropdown-tracker');
  let popupTracker = makePopupTracker(parentTracker);
  setContext('parent-dropdown-tracker', popupTracker);
  
  // Svelte action to add and remove the popup Element in the popup tracker.
  function addToPopupTracker(node: HTMLElement) {
    let elementExists = true;
    if (closeOnClickOutside) {
      setTimeout(() => {
        if (elementExists) {
          window.addEventListener('click', handleDocumentClick, {
            capture: true,
          });
        }
      });
    }

    popupTracker.register(node);
    return {
      destroy() {
        elementExists = false;
        if (closeOnClickOutside) {
          window.removeEventListener('click', handleDocumentClick, {
            capture: true,
          });
        }
        popupTracker.unregister(node);
      },
    };
  }
  
  let open = false;
  
  function handleDocumentClick(e: MouseEvent) {
    if (
      !popupTracker.contains(e.target as HTMLElement) &&
      (e.target as Node).getRootNode() === document
    ) {
      open = false;

      // Don't let anything else handle this.
      e.stopImmediatePropagation();
    }
  }
  
  // Code to set this up omitted for brevity.
  $: if (tippyInstance) {
    if (open) {
      tippyInstance.show();
    } else {
      tippyInstance.hide();
    }
  }
</script>

<slot name="button"><button type="button" on:click={() => (open = !open)}>{label}</button></slot>
{#if open}
  <div use:addToPopupTracker>
    <slot />
  </div>
{/if}