Email by Taxonomy Term
I found I can add an action handler that uses the select list to populate the Webform Permissions by Term element like I was thinking.

With a select list called Institution, using keys that match term keys in a taxonomy, the Update data with YAML section of the action handler can use this:

wf_permissions_by_term_element: '[webform_submission:values:institution:raw]'


The element gets updated on form completion and update, and individual result access is still limited by the Permissions by Term module.