If I'm understanding this right, and this basically an API that lets you pick which app store administers an app, that could be quite helpful, not harmful. I currently have fdroid, play store, and Samsung store, and I assume they try to update apps by the fully qualified name, as multiple stores show and try to update a single app instance, sometimes with weird results.
I don't think that's really what this is. This sounds like an additional warning screen, on top of the warning screen you already get when you manually install apps from anything other than the Play Store. I expect you'll still get the same old warning screen even after you pass this screen the one time.
FYI, if you have root there is a Magisk module that gives FDroid the privilege to install apps without the popup.
It shows every time you try and sideload a different app. Overall it’s probably a good idea but unlike every other warning on android there is no option to silence it forever.
It's also very obviously an attempt by Google to scare non-tech savvy people away from third party app stores and sideloading. Regardless of the actual risks involved, it's very beneficial to their bottom line if people fear anything "unofficial", so they're going to maximize every chance to reinforce that fear. A tactic Apple and Microsoft also use to great effect.
Honestly, I don't really see an issue with that. It seems no more annoying than Windows UAC or Linux sudo popups. It's a reminder that your app may have some behavior that you wouldn't expect from the regular sources. Mainly that it may not get regular updates along with the rest of the apps on your phone.
Of all the annoying things that Google and Android do this is pretty minor.
I really hope this will just replace the update dialogue, not add another one on top of it. Manually tapping "update" for all Fdroid apps is a huge slog already
My understanding is that this dialog won't appear if you update apps from f-droid or other 3rd party store, but only if:
The app was installed from one store (or just the play store, not sure), and
You are now trying to update the app by downloading an apk from somewhere else (e.g. a browser)
That would normally fail because the signatures don't match, but I guess there are places, like apkmirror, where you can find apks that are signed by the original developer (and so, they are authentic and 100% safe), but then google will give you a warning that you might not receive updates and such.
At least, that's my understanding. A tiny bit annoying, but not a big deal.