I'm pretty sure they're Group 31, the ones I used were these cheap Weize 100ah ones:
WEIZE 12V 100Ah 1280Wh Lithium Battery, Group 31 Deep Cycle LiFePO4 Battery for Trolling Motor, RV, Solar, Marine, Camping and Off-Grid Applications
www.weizeus.com
They're 13*6.77*8.46 inches and fit perfectly into the existing trays, those seem nice to get an extra 40ah per battery (if they're actually 140ah)
For connecting the AC outlet to the inverter, I don't think you'd really need any bigger gauge battery cable. Mine is 4 gauge into a 1/0 combiner that then runs to the inverter. It's pretty short, for 2000w you should be 100% fine. I've been looking at upgrading to a 3000w inverter and trying to squeeze a 4th battery in which would need 4/0 cable.
Honestly the AC only draws ~800-900w max anyway, so it's not like you're going to be drawing a full 2000w. At a 5% drop supporting the max draw from those batteries (400a), 1/0 would be good for up to ~23ft, 2% drop ~10ft. I'd say you'd be 100% OK.
Let me know how those batteries work out, I'm still planning to swap out most of the electronics, fuse panel, etc with the Redarc Manager30+TVMS Prime+TVMS Rogue in a month or two once we stop using the trailer every weekend.