I created a regular test product just now (no subscription) and that works. It redirects to my thank you page URL as expected.
For the subscription, I am doing test mode transactions and yes, the subscription plan was created in test mode. I do understand I will have to create a new subscription plan for live mode once we get things working.
I enabled the debug log and tested the subscription again and now, lo and behold, it works! Not sure why it wasn’t working earlier (the blue circle would just spin forever). This time, it still spun for a little longer that I would expect, but eventually the redirect did happen as expected.