As @Owl-53 mentions, you should completely ignore the "Available" storage value since it is very misleading. It is unfortunate that Apple shows the "Available" space value everywhere within macOS. The Free storage space value it the most critical storage value in macOS which is only shown in Disk Utility and the Apple System Profiler (aka System Information).
When using Time Machine or a third party backup software, they utilize APFS snapshots for the backups. APFS backup snapshots is one of the most common sources for Purgeable space. However, another respected forum contributor @etresoft has mentioned APFS snapshots are not necessarily the reason for large Purgeable space these days with Sequoia, but I forget if he mentioned what now makes up the majority of Purgeable space. Apple has made a mess of this since it is not clearly documented or easily shown. With a file system like APFS, it is difficult to properly report some aspects of the storage usage, but hiding the most critical storage value Free space is a huge disservice to users.
FYI, here is how you can view APFS snapshots and even delete them.
View APFS snapshots in Disk Utility on Mac - Apple Support
I do not recommend deleting APFS snapshots unless that snapshot has already been transferred to the external backup drive unless you have less than 20GB of Free storage space....nearing 5GB. Bad things happen if you completely run out of Free storage space such as no longer being able to delete files due to how the APFS file system works (Apple never created a reserve space to prevent this from occurring).
@Owl-53 has done an amazing job explaining most of this. I just wanted to add a bit extra information.
Edit: APFS snapshots will automatically be deleted....generally after about 24-48 hours, but third party backup software may have other settings that can be configured or used.
Also, when you delete items, those items may remain within those hidden APFS snapshots until they are deleted (usually in 24-48 hours).