I went a step further and installed Temporary Containers. Unless the domain is a special one (and goes in a long-lived container), a new tab cannot share any content with other tabs. Whenever the tab is closed all site-related content is removed.

It's still a bit wonky because some sites do redirections, and it's not properly caught (unless there's some option I missed)

The next step is to disable _all_ cookies, even first-party, by default (unless I have a special relationship with the domain of course). It's working surprisingly well and I believe this should be the default.