How do I recover free space after deleting files on a Mac Studio?

an additional issue users sometimes encounter if they have Time Machine active:

The space those files occupied can not be freed if they were part of a Backup that has not yet been written out to your backup disk.

So connect your backup disk and allow Time Machine to write out the files, and after a while (said to be a few hours to a day) the space will be freed.

The storage in the modern Mac is SSD storage. This stuff works a little differently that the old HDD and when files are deleted it may take time for the device to free up and make that space appear to Finder and Disk Utility as being free. Emptying the Trash and rebooting the Mac are a good start, but it still may take 24-48 hours or so before all the housekeeping shores are done.

Just to expand on a previous post

Unlike a traditional hard drive, an SSD can't simply overwrite existing data. 

Before new data can be written, the SSD must erase the flash memory cells that contain old data.

When you delete a file, the operating system typically just marks that space as available—it doesn't immediately erase the underlying data. 

Without TRIM, the SSD may assume those blocks still contain valid data and spend extra time moving and erasing data later, which can slow write performance.

macOS Tahoe  sends TRIM commands to the SSD indicating which blocks are no longer needed.

The SSD can then,

A - Mark those blocks as invalid.

B - Erase them during idle time.

C - Keep a pool of clean blocks ready for future writes.

This reduces write amplification and helps sustain performance over time

You will have to wait for the TRIM process to complete. It has to actually zero out the data that was stored there before it is available to be used for any other purpose. Gone are the days where on a mechanical drive, it just marked that location as available while the data remained until it was overwritten, with a SSD drive it has to be cleared first before it is available. That could time some time when you are dealing with that much data.