I have somewhat of the same issue, and have been trying for a few weeks to get help. I installed Opera on my Samsung Gear S watch and it was fine. Within 24 hours of getting my watch, it crashed after I tried to take my heart rate while running.
One of the results of the crash was that several of the app icons disappeared. Opera was one of them. The watch had to be reset. After the reset we tried to get Opera back on. There is something still on the watch that is fooling the watch and subsequently my phone, into thinking that it is still installed. There is no way to "uninstall" it, because it does not come up on the app screen, but it is not really gone.
I called Samsung to see if there was a way I could look at the file structure on the watch , and did hook it up to my computer but could not find any files having to do with Opera.
I need to remove that last remnant of Opera so I can reinstall it, as well. I have successfully installed other apps on the watch, so I know that the watch is functioning well. This is an Opera issue.