How can the browser tell the difference between a random thing you want and a random thing you don't want?

The permissions mechanism.

this is not a solution. Running an untrusted software will always be a security drawback. Permissions/sandbox/etc can decrease risk, but not eliminate it

Significantly reducing the risk is enough for me in many cases. Chasing “zero risk” is often a fallacy.

Expressing intent is good enough for me for this purpose. I understand that there are additional implementation specific risks.

How can the permissions mechanism be fine grained enough to prevent bad random things, and coarse grained enough that you can understand it?

Requesting site access by click or by URL really isn't rocket science.

Not nearly every user will get it right, so extensions will probably still have to be monitored for malware for the foreseeable future, but it gives many users at least a chance at privilege minimization.

Have you seen AWS IAM?

Power users who care about this don't need a GUI - a text file config in any format will do. Especially in this era of LLM assistance.

Create a new profile, do the niche thing there, separately from the rest of your browsing.