I see there was no response to your question in nearly a year. Were you ever able to resolve it?
I am seeing exactly the same thing on my Pi 400. I can boot Raspberry Pi OS fine, both 32-bit and the 64-bit beta, and UbuntuMATE 20.10, 32-bit and 64-bit. Ubuntu Server 20.04 64-bit also boots fine.
UbuntuMATE 20.04 gives me the behaviour you describe, with both the 32-bit and 64-bit versions. I have tried a number of different screens so I don't think it's an HDMI issue. Similarly, I have used several different SD cards, all of which have been tested with other OSes.
Since 20.10 is no longer supported by updates, this leaves those of us who want to use UbuntuMATE with a problem until 21.04 comes out. And we won't have an LTS release until 22.04 (probably not until this time next year).
Since I'm happy with 20.04 on my other machine (x86-64), and since 20.04 is supported until April 2023, I would very much like to get the 20.04 version for the Pi 4/400 working. It seems strange that we cannot, and that this issue has received no attention.
BTW I updated the Pi 400 eeprom firmware to the current version and that made no difference to the boot failure.