Fdroid installed apps will show up in yalp, they’re offered but should not install unless under typical conditions.
There are work arounds that allow an update to install no matter what, by disabling package signiture check; Lucky patcher or an exposed module do offer this. Some use it unknowinglynthat it’s not recommended for security reasons.
I use Aurora Store it is an alternative play store like Yalp. Having a filter feature that removes installed Fdroid apps from the aurora store installed app list which stops update notices and offers a blacklist too.
A user can disable the update feature but that thing called “convenience” goes to the wayside.
You can turn off Google play store notifications AND turn off auto-update in Play store settings. Then opt to check for updates manually; or use an alternative play store (ie.Aurora store) to offer updates.
If you are rooted, titanium backup app has a feature that detaches marketplace links from the play store.
Keep in mind that Google app store was designed to be the only store on a device. F-droid will not be able to circumvent it’s features without creating a securing issue.