You're not wrong about the state of the market for CS grads, I'm sorry anyone has to graduate into this. If it helps (it probably doesn't), I suspect we'll see a swing back to hiring humans in a few years as LLM costs go through the roof, and results fall short. Keeping your skills sharp and relevant, and extending them, will be a challenge.
If you have a plan to leave the US and try living elsewhere, but you parents don't think leaving is a good idea, have you tried pitching it to them as a temporary thing, like a gap year, to broaden your experiences, and maybe even get sone work experience? Even if you have no intention of returning, putting in in terms that your parents might be more comfortable with may make them more amenable to it, especially if you can imply that learning that they're right, and the US is the best place, is a likely outcome. Then, when you've been overseas for a year or two, you can tell them you've found a place you're happy.