Does this have any privacy implications? ISTR Google made it very hard to remove Google stuff even from Chromium.

Not that much, just the brand and some less calls to home (but chromium still calls home)

You cant run browser extensions in your electron app, but you can in the website version. So for privacy, expect more tracking, fingerprinting and less control. That's not the case for Jitsi, just in general all electron based website wrappers.

If Chromium still calls home, does that mean the MSFT has to remove all that code to turn it into Edge?

If so, that seems like a lot of work. Especially if you want to verify that it’s removed for future versions.

No, they just have to edit it so it calls home to them.

Still a lot of work though :P

exactly, see: https://github.com/Eloston/ungoogled-chromium