Or maybe F Samsung? Because I have a Pixel 2 running Android 11, and it made no difference to which apps can use different notifications. Basically if the app developer included an option to choose you can, and if they didn't then you have to use the system default tone (but I can choose one of mine for that: any sound file you put in the Notifications folder in your internal storage can be selected by the system sound picker. and I can choose a different sound picker if I want).

I don't use Zedge, and don't know what Samsung might have done in A10. But as someone who's OS is provided entirely by Google, rather than Google + Samsung, A11 is no different from A8, A9 or A10 as far as notification tones is concerned.

So maybe if you tell us what you used to do that no longer works?

 

It's surprisingly hard to be unambiguous when typing short messages, because your context is not the same as the reader's. Even now I'm not quite sure what "even by app" means: within the app whose notification you wish to change or using a different app? And assuming the latter is that using this other app as a sound picker (when you select to change the notification you can choose which app you use - provided you don't set one of them as the default) or in some other way?

Anyway, have you put your notification tones in a folder called "Notifications" in your internal storage? That's been the standard place to put them for at least the last decade, and still works in Android 11. If that isn't working on your phone then that's something that Samsung have done, it's not Android. In that case maybe see if you can work out what app is being used as the sound picker (the thing that allows you to choose a sound clip when you try to set a notification tone), locate it in Settings (I believe Samsung rename the submenu as "App Manager" rather than just "Applications" or "Apps & Notifications") and clear any defaults for it - if you can do that it ought to ask you which app you want to use, and then you can see whether something else (a file browser, Zedge, whatever) can do a better job.

Good luck.