If (only happens sometimes) you goto the URL opera://about or opera://update to check for updates and after an update's download is finished you get a Windows dialog from the Opera installer asking if you want to install the update, close Opera before choosing OK or Yes on that dialog. Otherwise, the update can fail because Opera is open.
Another thing you can try when you don't get that dialog (which is most of the time) is after the "relaunch" button appears on the update/about page, wait 30 seconds or more before clicking it. Or, if you have a hard drive activity light that you can watch, you can wait till it settles down to know when Opera is really ready to relaunch.
Another thing you can try is to not click "relaunch" on the page and instead close that page, close Opera yourself, wait 30 seconds and start Opera yourself. Sometimes having the update or about page open and checking for updates when Opera starts can mess with things.
Another thing you can try is if you restart Opera and it's still the old version is to just close Opera and start it up again.
Long story short, things work fine most of the time, but updating can be a little quirky in some rare cases.
If all that fails, you can download the offline installer ("Opera_136.0.6008.80_Setup_x64.exe" from https://ftp.opera.com/pub/opera/desktop/136.0.6008.80/win/ is the latest for regular Opera at this moment), close Opera, uninstall Opera (but do not choose to delete your data when uninstalling), delete the install folder afterwards (the "Opera" folder in "C:\Users\yourusername\AppData\Local\Programs" or "C:\Program Files" depending on whether you had a current-user install or an all-user install), launch the installer, click "options", adjust everything how you like and install. That should fix things.