As far as I can tell, the Batch Update app uses the React Select library to handle input components for single-select and multi-select fields (both “regular” and “collaborator” types).
Can the source code for the Batch Update app be made public so other developers can replicate the appearance already used in a “standard” Airtable app? As it stands, the Select component provided in the Airtable SDK isn’t quite sufficient for multiselect fields.