I'd start by treating this as two separate permissions: what information can go into the service, and what actions it can take. Chat access doesn't need to come bundled with connectors or permission to send emails.
Set a few clear data tiers. Public material and ordinary internal work might be suitable for an initial pilot. Student records, HR files and financial data should stay out of prompts and connectors until there's an approved workflow and logging you can actually use. Put an owner on each exception and make leadership explicitly accept the residual risk.
For actions, start with human review before anything is sent or changed. Give people a sanctioned option and plain examples of what they can and can't submit. That won't eliminate shadow AI, but it gives staff a usable alternative.
42-teeth-per-gear:
Include old shared drives and inherited folder permissions in that review. Those are easy to miss when testing only the current team spaces.