Current data scientist here, working for a cloud consulting firm. Two things stand out from my experience: (1) my company isn't hiring, while the DS team is doing fine revenue wise, the rest of the company is doing poorly; so uncommunicated moratorium on hiring; (2) I interviewed at an AI company that I'm currently subcontracting under - and they like me - and I didn't get past the first round because their requirements are so high right now (aka I did mediocrely on one interview and that was enough to tank me).
All this is to say, GenAI is booming but there's competing factors going on for businesses to hire.
Also a different take, look for contract jobs. As with (1) above, my company isn't hiring FT but they're open to contractors.
I wish you luck.