Locating hidden Time Machine backups on MacBook Pro

Open Applications > Utilities > Disk Utility, in the View menu select Show APFS Snapshots. You can select them and click the (–) button at the bottom.

@Grant Bennet-Alder, my Mac backs up hourly to a local NAS but I still see 47 GB of local TM snapshots. TM saves the last 24 hours plus a one-week old backup locally, at least when connected to an NAS. Those backups remain there after my weekly connection of one of a pair of 4 TB SSD that are my secondary TM backup. When entering the TM browser, that is evident because those backups load immediately even as the drives on my NAS are spinning up, after which older backups populate the browser. For my 2 TB internal storage, 47 GB is not a lot but if I were running a 256 GB Mac that would be an issue.

Backups are typically stored on an external drive.

All that writing of backup files to a slow external drive was found to consume a lot of I/O time, so Apple made a shift. In more recent macOS, the pointers to the files needed for the next backup set are now pre-collected in a snapshot disk image file. If you do not provide a physical drive soon enough, you may have several of these snapshots saved on the boot drive. They may not be on the MacOS volume.

But please, DO NOT delete them! instead, connect a physical backup drive and allow Time Machine to save some of them. Once saved onto an external physical drive, they will be deleted from the boot drive automatically.

If you do not have a recent local, disk-based backup, your computer is like a ticking Time bomb. You are only one disk failure, one mainboard failure, one crazy software, or one "oops" away from losing EVERYTHING! Drives do not last forever. It is not a question of IF it will fail, only WHEN it will fail.  In addition, you never know when crazy software or Pilot Error throws away far more than you intended.

A major upgrade of MacOS re-writes over 350,000 files. You should ALWAYS have a local disk-based backup on hand before you do a major software update.

About Time Machine local snapshots - Apple Support says:

Time Machine saves one snapshot of your startup disk approximately every hour, and keeps it for 24 hours. It keeps an additional snapshot of your last successful Time Machine backup until space is needed.

You can demonstrate that for yourself by booting Recovery > Restore TM Backup, and when selecting the restore source select the boot volume. It will show you all restorable local snapshots. If the source volume has sufficient space that last successful TM backup (implying, the one written to the TM backup disk) will be one of them, which can be more than 24 hours old.

<< TM saves the last 24 hours plus a one-week old backup locally, at least when connected to an NAS. >>

Based on that observation, would this be reasonably correct to say:

In a addition to what is stored on the backup disk, Time Machine appears to save 24 Hours of hourly snapshots (plus possibly the last weekly snapshot) as local snapshots on the Boot Volume, and

automatically removes the rest of those snapshots from the boot Volume??

Tthanks for the explanation and the link to that article.

It has another notable quote useful to answer a different complaint.

"I have just enough room on my disk for the downloaded installer. why can't I install?"

<< And in macOS High Sierra or later, another snapshot is saved before installing any macOS update.>>

Thanks! So in my case, it's keeping 24 hours of backups and the 'last successful backup' to each destination (I have three TM backup disks, the NAS and two SSDs so I can swap one weekly to my desk at work). Makes sense.

I was about to post a link to my "small space workaround" technique but thought better of it since we don't know anything about OP's MBP.

How to upgrade MacBook Air? it says not enough space - Apple Community

That was a real problem with 128 GB MBAs, which had barely enough room to begin with.

I don't like the idea of deleting local snapshots at all, ever, for the reasons you stated.