Hi, @Zero (Daniel Mcvittie)
The official Ubuntu MATE Download web page - https://ubuntu-mate.org/download/ - has 2 download sections/boxes for the Raspberry Pi (one for 32-bit and the other for 64-bit) :
Raspberry Pi
32-bit. Compatible with models: B2, B3, B3+, B4 and 400
[ Link: https://ubuntu-mate.org/download/armhf/ ]
Raspberry Pi
64-bit. Compatible with models: B3, B3+, B4 and 400
[ Link: https://ubuntu-mate.org/download/arm64/ ]
If you click on either the 32-bit or the 64-bit download links for the Raspberry Pi above, you'll see that the only Ubuntu MATE version currently available in those web pages is the 22.04.1 LTS (Jammy Jellyfish). So, I'm a bit confused when you write that you have "(...) downloaded [21.10] from the official site (...)". What web page did you use to download 21.10? May I suggest that you download and use the 22.04.1 version instead?
You may also want to read the "Raspberry Pi Installation Guide | Ubuntu MATE" - https://ubuntu-mate.org/raspberry-pi/install/ - if you haven't already.
I hope this helps