So no solve from Squarespace on this?
For me, it seems Squarespace does not like the "." punctuation at the end of an email server value for the MX records.
This is also reported on Apple's forums (https://discussions.apple.com/thread/254973529?sortBy=best) and another Squarespace forum thread:
I also had to configure another custom iCloud to a domain registered through Gandi and they accept the "." punctuation at the end – setup took less than a minute.
Maybe the true solve is to transfer my domain to another service...