A coworker of mine just had the same problem. I did not find any useful information in the logs. I asked my coworker to go to the AppData/Roaming/Docker/extensions directory and delete localstack_*. That failed with Windows giving the error of a file being in use. Interesting, since Docker was not running at that time.

Next, I had my coworker open Task Manager and look for running Docker processes and kill them. I saw localstack processes running -- five of them -- when I expected 0. I asked my coworker to kill off the localstack processes, reset Docker Desktop (perhaps an unnecessary step, but we were working off a fresh Docker installation anyway), and reacquire the LocalStack Extension. This worked.