You can copy a shared link and use the browser url bar to open it in a private window, or delete the extra crap at the end of the url (anything after the ? in a lot of cases).

Granted, that doesn't help for the service you're using to communicate with people (phone provider, real time chat service, email provider, whatever) and/or store your contacts. Especially if you're talking to someone who, say, hasn't turned all the creepy Gemini stuff off in their Google account and it's scanning all their emails and learning the names and emails of everyone they talk to.

Or any app that has location permission and can detect that you're in the same place as someone else.

I'd think they can probably figure it out by time too, after enough shared videos. Like, see that when x account opens a video, then y account also opens that same video within such-and-such an amount of time, or vice versa.