Good news! I have updated to Android 14 (Lineage OS 21). This means that I can now address a few issues (such as restoring keystore) promptly.
Using App Manager, I was able to restore most apps just fine (from Android 11 backups), except a few apps such as Molly (Signal client), SchildiChat (Matrix client), DAVx5. The first two have Android KeyStore dependency which does not yet work in Android 12+ in App Manager due to a new design scheme. The last app depends on Accounts.db which is not yet backed up by App Manager.
Using App Manager, I was able to restore most apps just fine (from Android 11 backups), except a few apps such as Molly (Signal client), SchildiChat (Matrix client), DAVx5. The first two have Android KeyStore dependency which does not yet work in Android 12+ in App Manager due to a new design scheme. The last app depends on Accounts.db which is not yet backed up by App Manager.