I can't say that I have much advice for this, but if you're serious about this, it's probably a good idea to contact a lawyer, maybe try this:
https://www.stratulat-albulescu.ro/en/contact/ I imagine a few hours of discussions won't cost you an arm and a leg and you should be able to get far more qualified advice than what you'd get from a rando on the internet.
If you do want to move, personally I would avoid Bucharest... a bit. Competition is super fierce. Timișoara, Cluj or Iași, especially Iași, should have a decent talent pool and slightly lower salary expenses/lower cost of living, and they all have international airports so you can easily move around when needed.
I'd learn a bit of Romanian. If you only speak English it will be relatively hard, but reasonably doable: https://www.openculture.com/2017/11/a-map-showing-how-much-t... (note: those numbers are for career diplomats undergoing intensive training, however, as you can see, it's still one of the easiest languages to crack for an English speaker :-) ).
