Dropdown closes on option selection when used in shadow DOM

Describe the bug

When using this library inside a shadow DOM (e.g. inside a web component), the behavior of the dropdown is different compared to when used in the "normal" DOM. When selecting an option, the dropdown disappears.

Reproduction

Here I created two custom elements, one without shadow, one with shadow DOM. Note the difference when selecting a selection option.

https://stackblitz.com/edit/vitejs-vite-czjnxx?file=filter.js

Expectation

Behavior of the dropdown should ideally be consistent and should work the same inside and outside the shadow DOM.

Environment Info

System:
    OS: Linux 6.5 Ubuntu 22.04.4 LTS 22.04.4 LTS (Jammy Jellyfish)
    CPU: (8) x64 Intel(R) Core(TM) i7-8550U CPU @ 1.80GHz
    Memory: 4.61 GB / 15.38 GB
    Container: Yes
    Shell: 5.1.16 - /bin/bash
  Binaries:
    Node: 18.18.2 - ~/.nvm/versions/node/v18.18.2/bin/node
    Yarn: 1.22.21 - ~/.nvm/versions/node/v18.18.2/bin/yarn
    npm: 9.8.1 - ~/.nvm/versions/node/v18.18.2/bin/npm
  Browsers:
    Chrome: 124.0.6367.201

Validations

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Check that this is a concrete bug. For Q&A open a GitHub Discussion.
The provided reproduction is a minimal reproducible example of the bug.

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vitejs-vite-czjnxx (Open reproduction)

I never work with Shadow DOM, if you know how to fix then please provide a Pull Request because I will most probably not look at fixing this myself. All the code is in MultipleSelectInstance.ts

I also assume that you meant (but forgot to mention) that the problem is for multiple selection? Because a single selection will of course close the drop right after selecting

After some digging, it seems that the target in

multiple-select-vanilla/packages/multiple-select-vanilla/src/MultipleSelectInstance.ts

Line 268 in 2f1d438

    
           (e.target === this.dropElm || (findParent(e.target, '.ms-drop') !== this.dropElm && e.target !== this.elm)) &&

behaves differently than with non-shadow DOM. When used inside a shadow DOM, the true event.target is masked and the parent element is returned instead. It is recommended to use event.composedPath()[0] instead of event.target in this case.