That looks like you're running the procedure in DEBUG mode, without any breakpoints. At least, those messages about connecting & disconnecting are consistent with that manner of running a procedure (it connects with another connection/thread).
If you just ran something like the following in a SQL Worksheet, you'll get a different message, maybe more of like what you're expecting:
Run it using F5 (Run Script). It'll give you a message like "anonymous block completed".