Yep all 3 are valid, matte is the new variant. https://www.etymonline.com/word/matte#etymonline_v_9722
And I’ve seen all 3 in use in the USA. It’s not matte = Canada. I’ve seen matte more than mat which is historically the spelling. The oed doesn’t list matt as the proper spelling but who knows with the brits.
Heh in German the word for gloves is literally hand shoe. So you’ve a very German pov.