UX is a great area to work in.
My impression is that it can be hard to get the first job as a junior, but once you have that first job, there's a lot of demand, and as you get more experienced you have a lot of choice of jobs, permanent or contract.
The contract ones can be very lucrative (though the contract market has changed a lot). With the perm ones there's a great future as you can move up the ladder from junior to senior to lead to manager, and then go on to manage big digital teams and projects if you want to.
But I think you have to be quite persistent to get that first job as a junior when you are freshly trained. You probably have to be open-minded to doing some work for little money to get stuff on your CV, or get lucky, or just be very persistent, determined and thick-skinned at the early job-seeking stage.
Some bits of this article are interesting - xd.adobe.com/ideas/career-tips/how-to-get-into-ux-design/#:~:text=But%20even%20with%20the%20high,your%20first%20junior%20UX%20position.
You get people from all sorts of backgrounds that come to UX. Backgrounds include uni / non-uni / customer services (phone operators) / developers / arty people / mathsy people / sciencey people
There can be some snobbery within some companies re certain degrees (ergonomics) or having a masters degree in research, but not every company has those requirements.
The need for UXers will only grow, I've already seen it grow in the last 12 years.