Help for "NOT Enough free space on this computer to back up iPhone." issue

I found a solution that worked for me in the thread https://discussions.apple.com/thread/7877727, titled "NOT Enough free space on this computer to back up iPhone. How can this be true when i have 194 GB available on the computer and my entire iPhone has only 118 GB used?". The thread is locked due to old age so I can't contribute there.

I had an iPhone with only 100 GB of data on it, and my Mac had 150 GB free drive space available and I was getting the same error. This worked for me and allowed me to back up my iPhone to my Mac. (Phone is iOS 14.1, Mac is Catalina 10.15.7)

First, I freed up even more hard drive space. I emptied my trash. I eliminated some large files by using About this Mac, Storage, Manage, Review Files; sorted the resulting Finder window by file size, and deleted stuff I could part without. I removed some big apps like Xcode that I can always download again. I ran a few utilities I had (CCleaner is one free example) to clean up cookies, browser caches, temp files, etc. Deleted my trash again. At this point a phone backup attempt gave me the same error.

I also freed up space on my phone to make its used space smaller, which would result in it needing less space on the Mac to store the backup. To free up space on the phone, I went to Settings, General, iPhone Storage, Review Large Attachments. It presented me with a lot of large photos and videos that I've already sent people via Messages, and I know they're in my Photos app, so I don't need them in two places. But beware, you can also delete photos/videos that are ONLY in messages, so if it's important to you, save them to your photo roll first before deleting them from iMessage.

In my Finder screen, selected my phone on the left sidebar, then chose Manage Backups. The list showed me some very old backups that I knew were no longer relevant (and I forgot why they existed) so I deleted them. I also deleted the most recent backup, which I normally wouldn't do since taking a new backup will replace it, but just to be thorough... At this point I still couldn't perform the backup--same error about not enough free hard drive space.

Well at this point the devices where just overwhelmed and confused. So performed a full proper power-off on the iPhone and a Shutdown on the Mac, and left them off for a few minutes. After starting them both up, I was able to perform the backup successfully.

I am not saying the solution is to simply shut down both devices. I'm saying the entire solution might be: delete crap from phone, delete crap from computer, confirm free space on computer hard drive is way bigger than used space on phone, then do a full and proper shutdown/restart on both devices.

I hope this helps the next person with this problem. :)