Technically by how an app has been installed (which store, via web browser, any other app or via adb) is just a data flag once that app has been installed.
If an app is available in two stores at the same time with identical signed versions there should not be a problem even switching the stores randomly.
Problems can only arise if the app to be updated has a different versionCode (e.g. a fixed offset) in one store.
The versionCode is a number internally by Android to prevent users from downgrading an installed app. App updates can only be installed if the app signature is created by the same developer and the versionCode is greater than the installed app version.
I have seen developers that have different variants of one app (for different devices, platforms, CPU types...) where each app variant has a different versionCode.
For example the one app variant has versionCode 0x2000234 and a second variant has the versionCode 0x1000234.
Both app variants show same version string to the user but internally looking at the versionCode they are totally different.
It may now happen that if the app in the store A has the versionCode 0x2000234 and the same app of a slightly different variant has the versionCode 0x1000234 in store B.
In such a case you could install the app from store A as update of the app in store B but not the other way around.