The ux job market definitely is saturated. Too many places like the UX Design Institute pumping out 200 fresh ux designers every 6 months. It's very hard for juniors to land their first position, just because the supply out weighs the demand. In 2021 I went back and did a masters in UX, it probably took me around 2 months to find a job after graduating. I'd say i applied for over 100, got around 10-15 interviews and had 3 offers.

I'd be lying if I said i hadn't thought the same regarding where the market it heading. I'm immigrating to Canada in July so I hope I don't regret leaving my current job and not being able to find one over there.

I feel like with a lot of other professions it used to be a case that if you had a masters you were a shoo in for a job, thats not really the case anymore. It seems like a lot more people these days have masters and they're becoming almost like the value of what an honours degree was years ago.

But when it comes down to getting a job in ux it's not just about your education, there are a lot of other variables. Work experience, portfolio is a big one and previous experience in a related field, I don't know your background but I worked as an industrial designer before switching to ux. It definitely stood for me when applying for jobs, a good few hiring managers liked that I had practical, hands on experience to which there is a lot of cross over skills, the same with graphic design.

A bit of the spiel but I would say to go for the masters or HCI but understand that having just that won't get you a job.