Overhead space prevents installation

Collecting partition information...
  System disk: disk0

Collecting OS information...

Partitions in system disk (disk0):
  1: APFS [Macintosh HD] (494.38 GB, 6 volumes)
    OS: [B*] [Macintosh HD] macOS v14.4 [disk3s1s1, 275C4265-9FC1-4544-B3D3-460BF2BC4D20]
  2: APFS (System Recovery) (5.37 GB, 2 volumes)
    OS: [  ] recoveryOS v14.4 [Primary recoveryOS]

  [B ] = Booted OS, [R ] = Booted recovery, [? ] = Unknown
  [ *] = Default boot volume

Using OS 'Macintosh HD' (disk3s1s1) for machine authentication.

Choose what to do:
  r: Resize an existing partition to make space for a new OS
  q: Quit without doing anything
» Action (r): r

We're going to resize this partition:
  APFS [Macintosh HD] (494.38 GB, 6 volumes)
  Total size: 494.38 GB
  Free space: 269.96 GB
  Available space: 0 B
  Overhead: 231.96 GB
  Minimum new size: 494.38 GB (100.00%)

  Warning: The selected partition has a large amount of overhead space.
  This prevents you from resizing the partition to a smaller size, even
  though macOS reports that space as free.

  This is usually caused by APFS snapshots used by Time Machine, which
  use up free disk space and block resizing the partition to a smaller
  size. It can also be caused by having a pending macOS upgrade.

  If you want to resize your partition to a smaller size, please complete
  any pending macOS upgrades and visit this link to learn how to manually
  delete Time Machine snapshots:

    https://alx.sh/tmcleanup

  Not enough available space to resize. Please follow the instructions
  above to continue.

I have deleted local timemachine backups to the best of my knowledge. I had to use the approach detailed here https://apple.stackexchange.com/a/340922 as none of the delete commands did anything. After running the command above there was only a single local timemachine backup remaining of the current date.

You can see that there is an overhead of 231.96 GB yet Available space: 0 B.

I had a look at this issue https://github.com/AsahiLinux/asahi-installer/issues/182 but I don't think it is exactly the same as mine. I'll try First Aid in the mean time.

EDIT: First Aid yielded nothing.

After assuming the issue had to still be to do with timemachine I ended up doing the following:

sudo rm -rf /Volumes/Backups\ of*MacBook\ Pro*
sudo rm -rf /Volumes/.timemachine/CA91C0E1-CD19-4808-948A-22FF4431ACE4/
sudo tmutil deletelocalsnapshots /

This managed to delete everything and the installer is now able to progress:

We're going to resize this partition:
  APFS [Macintosh HD] (494.38 GB, 6 volumes)
  Total size: 494.38 GB
  Free space: 271.24 GB
  Available space: 233.24 GB
  Overhead: 0 B
  Minimum new size: 261.14 GB (52.82%)

Enter the new size for your existing partition:
  You can enter a size such as '1GB', a fraction such as '50%',
  or the word 'min' for the smallest allowable size.

  Examples:
  30%  - 30% to macOS, 70% to the new OS
  80GB - 80GB to macOS, the rest to your new OS
  min  - Shrink macOS as much as (safely) possible

AsahiLinux / asahi-installer

Overhead space prevents installation #260