Delete everything in "C:\Windows\temp" and "C:\Users\yourusername\AppData\Local\temp" again.
Uninstall Opera again, but don't choose to delete your data when asked. Then, delete the "Opera" folder in "C:\Users\yourusername\AppData\Local\Programs".
Then, open up the Windows Task Scheduler, select "Task Scheduler Library' and look in the list for any Opera autoupdate tasks and delete them. There shouldn't be any since you uninstalled Opera, but make sure because it can cause problems in some cases if after you reinstall Opera there's more than one autoupdate task for Opera.
Then, in both "C:\Users\yourusername\AppData\Roaming" and "C:\Users\yourusername\AppData\Local", right-click on the "Opera Software" folder, goto "Properties" and click the "read only" box on the General tab so that it's clear (all white) and click apply. Then, switch to the Security tab. Make sure your username is in the user list and make sure it has full control (all permissions set to allow except for "Special Permissions"). Then, click Apply. Then, do the same thing for the "Programs" folder in "C:\Users\yourusername\AppData\Local".
Then, download "Opera_122.0.5643.92_Setup_x64.exe" from https://ftp.opera.com/pub/opera/desktop/122.0.5643.92/win/ in whatever browser you want, launch it, click "options", make sure "install path" is set to "C:\Users\yourusername\AppData\Local\Programs\Opera", make sure "Install for" is set to "Current User", adjust all the other options as you like and install.
That should take care of program file issues and permission issues for your profile files.
Updating should work fine from now on unless something is interfering with Opera's updater.
Then, to avoid some quirks with updating next time, if you have "Retain tabs from previous session" set at the URL opera://settings/onStartup, whenever you're on the opera://about or opera://update page and Opera shows the "relaunch" button when the update is ready, don't click it. Instead, close that tab and close Opera yourself, wait a tad bit and then start Opera back up yourself. The reason for doing things that way is to avoid Opera relaunching with the opera://about or opera://update page loading right away. If the timing is just right, the page can mess with Opera loading the new version.
As for the sync issue, if that doesn't go away after doing all the above, you should probably start over with a fresh profile for good measure. To do that, you can rename the "Opera Stable" folder in both "C:\Users\yourusername\AppData\Roaming\Opera Software" and "C:\Users\yourusername\AppData\Local\Opera Software" to "Opera Stable old" to start over. Then, before you enabled Sync, goto https://www.sync.opera.com/ in another browser, log in and click "Reset passphrase" to wipe out all your Sync data so you don't reintroduce any issues when using Sync again.
Now, if you need to save your passwords first, you can goto the URL opera://password-manager/settings and export your passwords to a CSV file and open it in a text editor to make sure they're there. Then, in the new Opera profile, you can go back to the same URL and import the CSV file.
For bookmarks, you can use the drop-down at the bottom left of the opera://bookmarks page to export them to an HTML file. Then, in the new profile, you can goto the URL opera://settings/importData, select "Bookmarks HTML file" in the drop-down and point it to the HTML file. Then, you can goto the URL opera://bookmarks, go into the "Bookmarks Bar" folder and move the imported bookmarks to where you want them.
That's all I would back up and restore so that you don't reintroduce any problems.
You might want to check your system files and check your file system. And, check the health of your drive with CrystalDiskInfo to make sure you don't have any corruption that causes Opera to get corrupted.