None of the solutions here would work for me. I have a keyboard issue from Vietnamese rain two years ago, and it means I cannot put my laptop in Recovery mode, or safe mode. So all the fixes were useless to me.
But then I found a blog post about Time Machine Snapshots that were possibly taking up space on my laptop.
See: https://tredje.se/dev/trouble/post/apfs-deleting-timemachine-snapshots-without-tmutil
Once the install fails, and you get the pop up window that says "not enough free space", click near the top of the screen until you get the drop down menus across the top. Under Utilities (I think that is what the tab is called) you will see Disk Utility and Terminal as options. Select Terminal, go to the blog post above, and follow the instructions.
If you're doing this, note that Step 6 had a small typo in it. I have altered Eric who wrote the post so he may update it. In step 6 he wrote: to enter this in Terminal => diskutil apgf listSnapshots BUT he means APSF as in => diskutil apfs listSnapshots
Hope this solves this super annoying and totally unacceptable error from Apple.