You can reset Google Sync at https://chrome.google.com/sync.
You can reset Opera Sync at https://www.sync.opera.com/ using the "Reset passphrase" link. Opera doesn't sync with Google's servers though. It only syncs with sync.opera.com and only extensions from addons.opera.com are synced.
For good measure, you should scan your system with the free version of Malwarebytes.
Also, look in "C:\Users\yourusername\AppData\Roaming" and "C:\Users\yourusername\AppData\Local" for a folder that's manifest.json in it. If you find one, open manifest.json in a text editor and see if that looks like the culprit. If so, delete the extension folder.
In the Windows task manager, see if there are any weird processes running. There could be malware running that keeps reinstalling the extension.
Check in "HKEY_LOCAL_MACHINE\SOFTWARE\Policies" for a "Google" key to see if there are any subkeys that are force-loading the extension.
Check "HKEY_CURRENT_USER\Software\Policies", and "HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Policies" too.
Check "HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Google\Chrome\Extensions", "HKEY_LOCAL_MACHINE\SOFTWARE\Google\Chrome\Extensions" and "HKEY_CURRENT_USER\Software\Google\Chrome\Extensions" too.
For Opera's desktop shortcut, right-click on it, goto "properties" and check the target field command on the "Shortcut" tab to make sure there are no command-line switched being passed to opera.exe to directly load an extension. Same with Opera's pinned taskbar icon by right-clicking it and right-clicking "Opera Browser" and going to "properties".
Check the "Startup" tab in the Windows task manager and "HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Run", "HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Run" and "HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\Windows\CurrentVersion\Run".
Searching for "olkpikmlhoaojbbmmpejnimiglejmboe" in the registry and removing things like you did will probably cover that, but you can manually check those keys just in case.
If a test standalone installation of Opera is not affected, but a regular installation is, you might have to uninstall the regular installation, delete its install folder and then delete/rename the "Opera Stable" folder in both "C:\Users\yourusername\AppData\Roaming\Opera Software" and "C:\Users\yourusername\AppData\Local\Opera Software".
You can goto the URL chrome://policy in both Chrome and Opera to see if it's picking up any polices from the registry. In Opera, you'll need to enable the "Show policy page" flag at the URL opera://flags/#policy first though.
