Hi Kavelach, welcome to the forums!
At the bottom of the Synapse-log, I see:
2022-10-05 21:02:06,225: WARNING - The user 'synapse' already exists
You could try removing the ‘synapse’ user, and then restore the backup again.
One way to check for the existence of a user, is looking in the shadow-file:
$ sudo cat /etc/shadow | grep synap
At the bottom of the Nextcloud-log, some missing directories are listed. Did you also restore the users? Maybe some users got deleted over time on the old server, without removing the directories for one reason or another.
2022-10-05 21:01:11,913: DEBUG - + ln -sfn /home/yunohost.multimedia/test /home/test/Multimedia
2022-10-05 21:01:11,914: DEBUG - + chown -R test /home/yunohost.multimedia/test
2022-10-05 21:01:11,916: DEBUG - + setfacl -RnL -m g:multimedia:rwX,g::rwX,o:r-X /home/yunohost.multimedia
2022-10-05 21:01:11,918: WARNING - setfacl: /home/yunohost.multimedia/share/Podcasts: No such file or directory
2022-10-05 21:01:11,919: WARNING - setfacl: /home/yunohost.multimedia/share/Playlists: No such file or directory
2022-10-05 21:01:11,920: WARNING - setfacl: /home/yunohost.multimedia/robert/Share/Podcasts: No such file or directory
2022-10-05 21:01:11,920: WARNING - setfacl: /home/yunohost.multimedia/robert/Share/Playlists: No such file or directory
2022-10-05 21:01:11,920: WARNING - setfacl: /home/yunohost.multimedia/test/Share/Podcasts: No such file or directory
2022-10-05 21:01:11,920: WARNING - setfacl: /home/yunohost.multimedia/test/Share/Playlists: No such file or directory
2022-10-05 21:01:11,921: WARNING - setfacl: /home/yunohost.multimedia/amelia/Share/Podcasts: No such file or directory
2022-10-05 21:01:11,921: WARNING - setfacl: /home/yunohost.multimedia/amelia/Share/Playlists: No such file or directory
2022-10-05 21:01:11,922: DEBUG - + ynh_exit_properly
2022-10-05 21:01:11,922: WARNING - setfacl: /home/yunohost.multimedia/synapse/Share/Podcasts: No such file or directory
2022-10-05 21:01:11,922: WARNING - setfacl: /home/yunohost.multimedia/synapse/Share/Playlists: No such file or directory
2022-10-05 21:01:11,922: WARNING - setfacl: /home/yunohost.multimedia/kacper/Share/Podcasts: No such file or directory
2022-10-05 21:01:11,923: WARNING - setfacl: /home/yunohost.multimedia/kacper/Share/Playlists: No such file or directory
2022-10-05 21:01:11,923: WARNING - setfacl: /home/yunohost.multimedia/laptop/Share/Podcasts: No such file or directory
2022-10-05 21:01:11,924: WARNING - setfacl: /home/yunohost.multimedia/laptop/Share/Playlists: No such file or directory
2022-10-05 21:01:11,924: WARNING - setfacl: /home/yunohost.multimedia/kavelach/Share/Podcasts: No such file or directory
2022-10-05 21:01:11,924: WARNING - setfacl: /home/yunohost.multimedia/kavelach/Share/Playlists: No such file or directory
2022-10-05 21:01:13,431: ERROR - Could not restore nextcloud: An error occured inside the app restore script
You could check whether the directories exist, and create them manually if they are not there.
If they are not needed, you can later remove the entries in Nextcloud and then from the filesystem.