How to continue Time Machine backups from a previous computer? I had MBP 2015 in the past and used Time Machine on it. Last September, I switched to MBP 16'' 2019 and did a fresh installation / manual copy of most of my home directory files, maintaining the layout.

Note: I wanted to do a fresh installation for various reasons but if I were to compare the filesystems in the end, they are almost the same – my home directory is still /Users/borekb, the folder layout under it is exactly the same, etc.

Now I'm trying to set up Time Machine again but I'd like to continue with my previous line of backups – for example, I want to see last year's versions of files that are on the same path. Also, my first backup on this new Mac should be &quot;incremental&quot; – I'd like Time Machine to compare what is on my current Mac with the latest state of my previous backups (from September 2020) and does a diff as usual.
The key to this seems to be the tmutil inheritbackup command, which I've successfully ran:
$ sudo tmutil inheritbackup /Volumes/time-machine/Borek’s\ MacBook\ Pro.backupbundle
Password:
Mounting disk image...
Unmounting disk image...
Inheriting disk image for machine...
Successfully inherited disk image '/Volumes/time-machine/Borek’s MBP 16.backupbundle'

/Volumes/time-machine is a mounted network folder (I backup wirelessly to a Synology NAS) and the command seemed to work well – it did this rename:
Borek’s MacBook Pro.backupbundle → Borek’s MBP 16.backupbundle
I then went to Time Machine UI, selected the time-machine disk, entered my previous password for encryption, etc.:

Everything seemed fine so far.
However, when I start backing up, it does a full initial backup to a new folder inside the .backupbundle that is called after my new computer's name: Borek’s MBP 16. This is what it looks like after I mount the sparse bundle and browse the /Volumes/Time Machine Backups/Backups.backupdb folder:

I somehow want to tell Time Machine keep using the original Borek’s MacBook Pro folder (the one that was last modified on 22 Sep 2020).
How to do that?

UPDATE 1: I tried changing my computer's name to match the old one but Time Machine still insists on creating a new set of backups from scratch – it just calls the new &quot;machine directory&quot; Borek’s MacBook Pro 2:

I have also ran this script, found here (as Big Sur doesn't seem to support -a), to run tmutil associatedisk an all folders found under the original backup location:
for f in /Volumes/Time\ Machine\ Backups/Backups.backupdb/Borek’s\ MacBook\ Pro/*; do
  if [[ -d &quot;$f&quot; ]]; then
    sudo tmutil associatedisk /Volumes/Macintosh\ HD &quot;$f&quot;/Macintosh\ HD;
  fi;
done

This also worked correctly but Time Machine still doesn't see my older backups and is attempting to create Borek’s MacBook Pro 2 when I try to run a backup.

UPDATE 2: I've successfully verified backups which was a solution in this answer. The preferences UI still report &quot;no backups&quot; so I'm now trying to run a new backup, which was Step 2 in that answer and the author wasn't sure if it's necessary or not. I'll report back in a few hours...
If you tap the option key while clicking the time machine icon in the menu bar, you can browse backups from previous or other computers.