KDE Connect allows me to browse the folder I picked and upload/download files just fine, using SAF. You point the app at a directory, click "grant access", and you have permanent access. The only problem I can think of is that some directories are restricted (https://developer.android.com/about/versions/11/privacy/stor...) because they're a dumping ground for files already.
SAF provides both provider and consumer APIs, and from the language NextCloud uses, I get the feeling they might've missed the consumer API here. Had NextCloud said "we want the user to be able to select the Download folder and certain external media directories" then I would've thought the restrictions are the main problem, but that doesn't seem to be the case here.
This is all guessing by me, but I think that, traditionally, there's been a certain quantity of users that synced folders out of the /Android/data or similar locations and/or needed some extra flexibility. When Android 11 arrived, it was difficult to break that workflow for all those users (and I guess there was also some re-architecture needed for the app, but I don't know how much would it be).
I went through the same with Syncthing, and now I install it from out of Google Play, where it doesn't need Google approval to do the All Files Permission API call.
I understand why the API changes and the hardening of the Android system, but it's also true you're locked out from certain folders even when on developer mode and it feels weird.
SAF provides both provider and consumer APIs, and from the language NextCloud uses, I get the feeling they might've missed the consumer API here. Had NextCloud said "we want the user to be able to select the Download folder and certain external media directories" then I would've thought the restrictions are the main problem, but that doesn't seem to be the case here.