We currently have an issue that is affecting some Gutenberg blocks but it seems that this also affects the Gutenberg PMS Registration block, I’ve also added this information to our development team and this issue will be fixed in one of our future updates to to Paid Member Subscriptions.
Regarding the member issue:
I’ve tested on my WP Instance with a setup similar to yours, but there everything works correctly (after registration the user is a PMS Member with a Pending subscription plan). Since this looks a lot like a conflict with some other code or plugin, the next recommended step is the conflict test (ideally in a staging environment):
Briefly* disable all other plugins and enable the default Twenty Twenty theme. Please also disable all add-ons. If this fixes the problem, enable everything one by one, checking each time to see when the problem returns.
Note: Please do the conflict test on a test site, not on the live site.
Important: Also with Paid Member Subscriptions, on the staging/testing site you need to activate Test Mode (from Paid Member Subscriptions -> Settings -> Payments page), and also to deactivate all the emails (from Paid Member Subscriptions -> Settings -> E-Mails -> and toggle off all the emails).