Now I found a good way to migrate data to another phone. After the tries with migrate helper and adb pull didn’t work, and Seedvault couldn’t be restored either, I had to look for a backup solution with root. So I rooted my FP3 with magisk on the /e/ recovery like described here.
Then I installed OandBackupX from f-droid (now NeoBackup). And I transferred the backup file to my new FP3, and did a recovery with OABX there. It worked just like a charm! Just two apps made problems. Matrix Schildichat I couldn’t transfer data. And Signal has now a migrate option in its settings, that works pretty well too.
Neobackup (and it’s predecessor) can also make scheduled backups, even on sd-cards. Pretty good stuff!
Minus points: You need root. And my bootloader is still unlocked. But such a good backup solution may be worth rooting.