The law and reality is that if you are married to a US citizen, you are entitled to residency.
In addition to having my own situation with my spouse, a next-door neighbor of mine had a similar situation. She was married to an undocumented immigrant.
Well, he got nabbed for a DUI and deported back to Mexico during Trump's first disgracing of the White House, but she appealed on the basis that they were married. ICE and USCIS tried to dissuade her by questioning her birth records, but that was bullshit and they eventually let him back into the country (and this was before Biden got in.)