I have a 3080 and a 5950x. I run a 27inch 1440P screen. I
had one of those inverter trolleys with 2x100ah deep cycle batteries.
While rendering my entire pc, with screens and modem used 550-600w
While gaming, about 500-550w
2 hrs of gaming means it requires 1000-1200w of real world capasity
2x100ah is theoretically 2000w, meaning you using 50% of capasity, which is considererd safe.
that being said. my battieries never lasted a year of gaming and working on them, even though i was careful never to discharge more than 50%.... increase from stg2 to stg4 plus... well that was the problem.
Whatever you do, get a lithium phosfate solution. maybe 2x100ah LiPo batteries at least. it will have to be a custom/trolley option. No ecoflow/all in one package will have that amount of available w/hours at that budget.
DO NOT GET GEL/LEAD ACID.... everyone raves about it until they dont.
#edit
@Lupus posted a good option earlier i see in budget