Updating Problem

See if you can download and apply this combo updater: macOS Catalina 10.15.7 Combo Update. The combo updaters are generally easier to use and, I've found, more reliable.

Just so we're on the same page and not misinterpreting what you're referring to the space on your drive is referred to as free space. Memory is the 8 to XX GBs that are added at the time of purchase or, for 27" models, afterward by the user.

Generally it is recommended to maintain a minimum of 25-30 GB of free space on your boot drive for optimal system and application performance. If one uses Photoshop or Photoshop Elements which needs a lot of temporary cache space on scratch disks then more free space is even better.

I have exactly the same problem. I must have tried 7-8 different times to update to 10.15.7. After going through the normal update sequence, when the screen comes back on, my computer is still at 10.15.6 and I have the software update message still on my screen.

Safe Boot, (holding Shift key down at startup).

Try the standalone 10.15.7 Combo in Safe Mode...

https://support.apple.com/kb/dl827?locale=en_US

Well, what you can do is try t update your mac from the Terminal:

$ softwareupdate -i -a --verbose
Software Update Tool

Finding available software