I always flip the switch, the big one.
https://admin.google.com/ac/owl/settings
Also, I never allow a difference between staff and students.

Nobody is allowed to give unknown third-party services full API access to anything. Admin does it = me.
If I'm being nice, I flip it after I've trusted or added the most important client_ids. Like the first 100 of those with the most usage AND documented to be (legally) allowed, and some that I know are very important for some services, but are perhaps not used by many.
The rest is left to just stop working. If someone truly needs those services you haven't already allowed, they will reach out and ask for it. To be smart, set up such a process before flipping the switch, and tell people about it.
We have a very simple Google Form, where the requester has to fill in a lot of information regarding the service, which a small team then evaluates. Also, only allow requests for access through that one and only process, and bring legal in on it. Regardless of who is asking.
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https://wheretofind.me/@NoSubstitute