The fact that it returns a 200 probably means that Invidious is properly up and running. Could you elaborate further on what you mean by "setup isn't completing"? How are you trying to connect to the web UI? Sharing your docker-compose.yaml might help us debug as well.
Edit: I just noticed that the default compose file has the port bound to localhost:
ports:
- "127.0.0.1:3000:3000"
which means you won't be able to access it from other machines inside or outside your network. You'd have to change that to - "3000:3000" to enable access for other machines.
To add to this, are you running docker-compose up with a -d flag?
When I got into Dockers, I got confused when the docker command would not complete (i.e. get back to bash shell after completing the command). In docker, you need to specify the "-d" flag to run it in background (i.e. separate daemon)
One more point, when @CumBroth@discuss.tchncs.de says
Ooooh, good catch. I assumed "it's been giving me the same message for over an hour" to mean that they've been monitoring the logs, not running in interactive mode. O_O