Others please correct me if I'm wrong but f you're not rooted (and don't have a system with backup like Seedvault) you're reliant on what backup functions the individual apps provide have. For a program to back up the data of other apps it needs root privileges (which is good otherwise apps could just read / write data of other apps).
You are correct. Apps have to opt in to support any backup of their private data. This is intended as a privacy measure.
The only way around it is to fundamentally break Android security protections.
How terrible, apps being able to read all the data on your device when you give them permission to do so. The restrictiveness of SAF is so annoying on Android.
'No you can't use this folder, and there is literally no way to bypass this screen. You just can't read/write to it.'
I'd pull the entire internal storage down to a hard drive/folder, as that's really the only stuff you can get at without root anyhow. These days, most things are tied to your Google account on Android anyhow, and what isn't, is generally stored locally.
Only apps with root can see the private app data in /data/data/ or /data/user/*/ that stores your app preferences, login info, databases, etc.
Without root, you can have some extra permissions by installing Shizuku - you will need adb to grant Shizuku those rights (this app is used to give those permissions to other apps supporting Shizuku - check those here https://github.com/ThePBone/awesome-shizuku ). For example Swift Backup works best with root, but without it it can still backup at least external app data (located in Android/data)
You used to be able to do proper backups via adb, but now you rely on app devs using proper backup methods via Google drive thing, and very few of them do.
Neobackup if you're rooting
If not... idk
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