You might be able to modify the extension to redirect away from opera://extensions (or prevent navigation to). Malware extensions often do that somehow. You could then pack the extension in a crx file.

Then, you can place the crx file in a spot that's read accessible by all users and modify all Opera's shortcuts for all users to use the --load-extension command-line option.

The command for all Opera shortcuts would look like this:

"C:\Program Files\Opera\opera.exe" "--load-extension=C:\OperaExtensions\extension.crx"

for example.

However, you'd also have to modify the command in "HKEY_LOCAL_MACHINE\SOFTWARE\Clients\StartMenuInternet\OperaStable" and "HKEY_LOCAL_MACHINE\SOFTWARE\Classes\OperaStable" to use "--load-extension" too (after each time Opera updates) so that if Opera is opened via a file or protocol association, the extension loads too.

Or, instead of modifying an extension extension, make your own extension to redirect away from opera://extensions and force-load your extension via --load-extension after the Tab extension is installed for all users.

All of that would be a mess to do though, if you can even get it to work.