There is nothing pushing her to leave whatsoever. Why would working a part time job at $500 a week achieve the opposite result? So what if she has some spending money, maybe she'll get an xbox and ps5, or a PC or something. The only way she'll consider leaving is if Phil expects her to be equal partners, because then there is no reason to put up with him. She might as well at that point move into a shitty apartment with some stranger. The appeal of him was "you don't need to pay bills, you just need to stick around", and if that is gone then nothing about it is worth it.
That is why Kat is never going to leave. Kat is a grifter with some MAJOR psychological issues that only many many years of therapy can fix. Kat TRIED to leech off of Subaru man, but even he got tired of her antics, until Mr. Gout ya girl came in the Twitter DM's and convinced some female from the MidWest to move in with him. You know he gave her a SWEETHEART deal: come live with me, you keep all of your part-time money, but you have to have to make sure everything is clean.
Also, remember when chat was mentioning "demon possessing.", Phil didn't know what they fuck they were talking about, but Kat got VERY VERY uncomfortable. You just don't pick up anything and have some random female move into your place, unless it's a roommate situation, and you screened her VERY WELL! Phil was able to charm her, fly her out, and showed her how her life can be easy. He'll pay all the bills, she'll get free room and board, her own room, and all she has to do is pay for her own DoorDash and try not to be break another $500 vaccum.
Phil has mentioned before they sleep in separate bedrooms because of his snoring. Leanna had no issue with that, but Kat does? I digress.
Kat is NEVER going to leave Phil unless she can upgrade to a bigger and better position. Do I see that happening? No. She has NOWHERE else to go, so, she's going to follow Phil until he dies and after that, Kat is up shit creek without a paddle.