If I’m not mistaken A13 / T is still on the old prebuilt seedvault version. Only a14 and up will use the upstream seedvault (14-4.1) that lineage ships.
In those Notes backup should get picked up after a few retries? SV will do the App apks by itself, independent of AppLounge - there really isn’t much to backup in AppLounge itself but your user choice Account or Anonymous.
As to “local contacts”, even if the backup would work/succeed, it will not include synced contacts (those that carddav/nextcloud/murena.io lists).
I can explain some more, but a green checkmark isn’t really a guarantee if the App isn’t written with the native Android backup in mind. There’s only some automatism to it.
In any case, for users on A14+ and not specific to your remarks: enable the device to device feature - behind a switch in the upper right 3-dot menu → expert settings - to override Apps that have useful backup settings, but disallow cloud backup.