Where is /timeshift?

Trying to set up timeshift to backup my system files, I managed to delete almost my entire home folder (Ah, the irony!!).

Fortunately, I fished out the deleted files from the disk with undelete-btrfs. Now I’m trying to restore everything to the state it was before, and I have some trouble understanding both what happened and what is going on now. In particular, I don’t seem to find the backup folder /timeshift.

According to the timeshift docs:

Snapshots are saved by default on the system (root) partition in path /timeshift. Other linux partitions can also be selected. For best results the snapshots should be saved to an external (non-system) partition.

I did a manual timeshift backup before deleting home, but it doesn’t show up in /timeshift:

~ » ls /
afs  bin  boot  dev  etc  home  lib  lib64  lost+found  media  mnt  opt  proc  root  run  sbin  srv  sys  tmp  usr  var

I find it in run:

~ » sudo find / -iname 'timeshift'
/run/timeshift
find: File system loop detected; ‘/run/timeshift/backup/root’ is part of the same file system loop as ‘/’.
/run/timeshift/backup/timeshift
/run/timeshift/backup/timeshift/snapshots/2022-10-30_15-24-36/localhost/etc/timeshift
/run/timeshift/backup/timeshift/snapshots/2022-10-30_15-24-36/localhost/usr/bin/timeshift
/run/timeshift/backup/timeshift/snapshots/2022-10-30_15-24-36/localhost/usr/share/doc/timeshift
/run/timeshift/backup/timeshift/snapshots/2022-10-30_15-24-36/localhost/usr/share/licenses/timeshift
/run/timeshift/backup/timeshift/snapshots/2022-10-30_15-24-36/localhost/usr/share/timeshift
/run/timeshift/backup/timeshift/snapshots/2022-10-30_15-24-36/localhost/var/log/timeshift
find: ‘/run/user/1000/doc’: Permission denied
find: ‘/run/user/1000/gvfs’: Permission denied
/run/lock/timeshift
/etc/timeshift
/usr/bin/timeshift
/usr/share/doc/timeshift
/usr/share/licenses/timeshift
/usr/share/timeshift
/var/log/timeshift

What is happening? What’s with the file system loop? Here is the output of lsblk, if it helps:

~ » lsblk
NAME                                          MAJ:MIN RM   SIZE RO TYPE  MOUNTPOINTS
sda                                             8:0    0 447,1G  0 disk  
├─sda1                                          8:1    0   529M  0 part  
├─sda2                                          8:2    0    99M  0 part  
├─sda3                                          8:3    0    16M  0 part  
├─sda4                                          8:4    0 445,9G  0 part  
└─sda5                                          8:5    0   581M  0 part  
zram0                                         252:0    0     8G  0 disk  [SWAP]
nvme0n1                                       259:0    0 465,8G  0 disk  
├─nvme0n1p1                                   259:1    0   600M  0 part  /boot/efi
├─nvme0n1p2                                   259:2    0     1G  0 part  /boot
└─nvme0n1p3                                   259:3    0 464,2G  0 part  
  └─luks-1b6f6060-d32a-4e89-8f56-8fd22ab3916e 253:0    0 464,2G  0 crypt /run/timeshift/backup
                                                                         /home
                                                                         /

I’ve never done this myself, but perhaps this conversation over on the discussion site might be useful reference?