Adding a folder to the Time Machine exclusion unfortunately does not exclude it from the local snapshots, it only removes it from the copy it does to the TimeMachine destination volume.
> Backup utilities including Time Machine normally make a snapshot with each backup, and retain them for 24 hours, following which they’re automatically deleted. As snapshots can’t exclude folders in the way that Time Machine can in its backups, if you’ve been working with a couple of 100 GB VMs then they will be retained in snapshots even though you probably exclude them from being backed up.
From https://eclecticlight.co/2025/10/02/why-did-that-macos-upgra...
> Backup utilities including Time Machine normally make a snapshot with each backup, and retain them for 24 hours, following which they’re automatically deleted. As snapshots can’t exclude folders in the way that Time Machine can in its backups, if you’ve been working with a couple of 100 GB VMs then they will be retained in snapshots even though you probably exclude them from being backed up.