[Remove Vuetify from Studio] Create public API and fine-tune autocomplete multi-select component

[MisRob]

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Description

Now when #5133 is set up, continue in learningequality/kolibri-design-system#1087 by adding public API suitable for all our use-cases, and also fine-tune the component.

[MisRob]

Closing as per learningequality/kolibri-design-system#1087 (comment)