Can we restrict the visibility to Contacts based on Territory Assignment?

Summary:

No option to view the associated Territories at the Contact level, unlike Accounts.

Content (please ensure you mask any confidential information):

We are trying to restrict the visibility of Contacts via Territory assignment. When a contact is created/updated, territory should be assigned to it automatically, and its members should be copied to the Contact team to have full access to the record.

Now, the issue is that the "Run Assignment" button at the contact level is greyed out, and I cannot find any scheduled process or profile option that assigns territories to contacts in bulk. Also, in the contact teams tab, we don't have the option to view the assigned Territories, unlike Accounts. This begs the question if the territory-based assignment is available for Contacts or not. If not, then how to control the visibility of Contacts?