If I had that problem I’d take it to the local auto machine shop and get their opinion. They have special tools and know-how & could probably solve that problem in a jiffy for not much $$.
Concur w/ @Barkydog for a diyer job, a nut splitter tool would probably get the job done pronto. Sears used sell them for not much $$$. That tool comes in handy quite often, I used mine recently on a plumbing problem, so it’s a pretty good tool to have on hand since it is so frugally priced.
hmmm … what else? If the bolt just slips through a hole (not threaded) and can be removed from either side you could cut the head off the bolt on the other side with a dremmel tool or just a short hack saw blade and patience, then pull the whole thing out from the nut side, or visa versa. That nut looks too damaged and damaged in an asymmetrical way, to bother with a bolt extractor socket imo.
There’s a thread here from several years ago you can probably find using the search feature which had all sort of ideas or removing stuck nuts and bolts. Search for a thread on stuck bolts or something like that.
Worse case you’ll have to remove the stuff that’s in the way.