The location used for auto save files has changed over the years, and in SketchUp 2019 and later it is in yet another new place. The most recent change was because the previous location was in a folder that your operating system might clear out overnight, which wouldn’t be a good thing.
There’s also some confusion about what an auto save file is, and what a backup file is. Below is a description of each, but first, a note about file paths…
File Paths
When posting a file path for Windows you might stay something like: “C:\Users\YourName\AppData\SketchUp\SketchUp 2019\SketchUp, change the YourName part to be your Windows user name”. Or: “Macintosh HD/Users/YourName/Library/Application Support/SketchUp 2019/SketchUp, change ‘Macintosh HD’ to be your drive name and YourName to be your Mac user name”. A significant amount of your post is to explain how to alter what you gave, in order to end up in the right folder!
Fortunately, Mac and Windows have a way to get you to the right folder without knowing the user name or the drive letter or name. Here are those two examples in that format:
%AppData%\SketchUp\SketchUp 2019\SketchUp
~/Library/Application Support/SketchUp 2019/SketchUp/
On Windows you can get to the intended folder by copying and pasting the path into File Explorer. On Mac you can either select the text then right-click and choose Services/Show in Finder, or you can copy the path and use Finder’s Go/Go to folder… menu, then paste the path in there.
Back to the main topic:
Auto Save
Auto Save is a feature that will save your currently open files every so often. You can choose how many minutes apart that is (in Preferences/General). The file is saved with the same name as the current file, but buried in a particular folder. Normally you would never need to visit that folder, because if SketchUp crashes, the next time you open the Welcome screen you will see the auto saved files in the recent files area, with each one having a red Recovered banner over the thumbnail.
What you should then do can get slightly confusing. If you choose to open the original file, you may be told that the recovery file is more recent, and are you sure you want to open the original. If you choose the recovered file, you will be asked if you are sure you want to use that one instead of the last saved version. Carefully read what you’re being asked, and then decide which one to keep.
Now that the folder used is not one that the operating system will clear out overnight, you can go and take a look what is in there, to most likely find some very old projects that had crashed at some point. These are the full paths for SketchUp 2019, that you can copy and paste into File Explorer or Go to folder:
%LocalAppData%\SketchUp\SketchUp 2019\SketchUp\working\SKETCHUP\RecoveredFiles
~/Library/Application Support/SketchUp 2019/working/SKETCHUP/RecoveredFiles
If you do look in there and find something you had otherwise lost, move or copy the file out of that folder before working on it. Otherwise working on a file that auto saves into that same folder could lead to some confusion about which is the current file.
Backup File
A backup file is created in the same folder as the current model file, but when it gets made is worth understanding. You might think that a backup file is similar to the auto save files, in that the backup will be updated many times between each save of the current model file. It doesn’t work that way.
The first time you save your file you will only have that one file, the backup file is not made for that first save. Subsequent saves will leave you with two files, one is a renamed copy of the previous saved file, and the other is a new save of the file. One main function of the backup file is for when you want to go off in one direction for a while, and decide it’s not an improvement, you could delete the current file and rename the backup file, to take you back to the point you started to make those changes, without having to do a lot of Undos.
The backup files are named differently on Mac and Windows. On Mac the file name has a tilde added, so MyModel.skp would have a backup of MyModel~.skp. On Windows the same name is used, but the file type is changed to be SKB. MyModel.skp would have a backup file of MyModel.skb.
Summary
If you have a crash that either leaves the file corrupted, or loses a lot of work since the last save, using the Recovered file from the recent files list would make sense, but be sure to test the model before doing a save. The problem that led up to the crash could already be present in the recently created auto save file, and the previous backup file may be in a better condition. If you commit to the recovered file and do a save right away, there is a chance that your previous good backup file will be replaced by a copy of the auto save file that already had a problem.
It is worth having your own system of creating backups for your project. One easy approach is to occasionally duplicate the file and rename the copy to include a version number or a date, or alternately, use File/Save a Copy As to save out a copy with that special name. Save a Copy As is different to Save As, in that afterwards you are continuing to work in the original file, and not in the newly created file.