Some extensions, such as SponsorBlock for YouTube actually limit themselves so they can only operate when the browser is on youtube.com. This can be declared in the extension manifest. It's a separate permission to access data on all web sites vs. access data on a specific website.

I used to rely on Consent-O-Matic a lot, but I'm somewhat uncomfortable by the fact that the extension has full access to all web page content. I mean I understand why, but I'm still uncomfortable with it. In the end I ended up uninstalling it because it broke some sites so that they wouldn't load at all, or got stuck into an infinite reload loop. On majority of cases it works alright though.

Sounds like a job for the Mullvad browser, since that clears cookies on every restart by default.