No chroot
. The filesystems may not even be mounted, or else fsck
will cause even greater damage!

And: In case a former check and repair using
gParted
may have removed some data, is it worth to restore /home/Username from anrsync
-backup? If so, how?
For that, you need to mount the /home
filesystem, and the one holding the backups.
Assuming that you’re working from the live USB — as you should! — first mount your /home
at /mnt
.
sudo mount -t ext4 /dev/nvme0n1p4 /mnt/
Then, you need to create a mountpoint for the volume with the backups. As I don’t know what volume that is, I will use /dev/sdb1
in the example below — adjust as required.
sudo mkdir /backups
sudo mount -t ext4 /dev/sdb1 /backups/
cp -RPpv /backups/timeshift/snapshots/<time-of-last-backup>/localhost/home/* /mnt/ && sync