Harden has no leverage to force his way to Brooklyn because they aren't in a position to sign him even if he goes to FA.

I mean, if the Nets trade Harris, Levert, and DJ for nothing/expirings by the end of the 2022 season and then Kyrie and KD opt out of their final year and all 3 of them take discounts to play with a bunch of vet min guys... Sure. Then they could do it (or Harden could just eat all of the millions fewer on his contract and play for a much smaller value than he is worth (again with nothing but vet min support).

Nothing about that sounds palatable or likely to me.

So the question is, if he can't get to that one specific team, does he want to leave Houston for another team that has to part with good assets to get him?

Unless Morey or some surprise team comes in and knocks the Rockets socks off (and I doubt Harden is excited about going to random teams unless they become legit contenders... Philly is really the only other realistic option), don't be surprised if money wins out.

I think it is likely that as long as Houston looks good this year, there is a very decent chance he just stays and takes the money.