One of my children was in a similar position. They picked their degree specifically because it was a skills shortage area. All through uni they were told "you'll have a job lined up by graduation, you'll be able to take your pick" which suddenly changed to "oh this is the worst year ever for jobs!"
They initially assumed they'd get a job in their uni city but none were advertised and it's too expensive a city to live in alone with the zero hours minimum wage job they'd had at uni. So they came home, assuming as we're also in a big city they'd find a job in their field here.
Anyway, the advice I gave to them was to treat applying for jobs as a full-time job in itself. They were doing a two-fold search: any work at all and a job in their field.
I also encouraged them to stay active, meet friends for a coffee, do a bit of DIY for grandparents etc. I didn't want them falling into a pattern of staying in bed/not seeing anyone.
I suggested they'd have more luck with jobs with unsociable hours - night shifts and whatever, and we'd work out the logistics afterwards. That paid off and they got a minimum wage hospitality job which gets them out of the house, keeps a bit of money coming in and padded their CV out slightly. Yes sometimes s it involves me picking them up at 5am because there's no buses, but it is what it is.
They ended up applying for any job in their field advertised nationally, rather than just commutable distances. Ended up getting a job after their 7th interview but in a city a couple of hours away so they'll have to move. Now, they could only do this because we're luckily in a position where we can pay their first month's rent and deposit, plus give them some money to tide them over until their first pay day. If you're in a position to do that, then make it clear to them that they're not on their own and you'll support them practically too. I know many people are rigid about this type of thing and believe in making young people stand on their own two feet, but given the difficulties in securing jobs I couldn't give two hoots - they're already moving away to a city they don't know, by themselves with no support network there. If you're not in a position to do that financially, think about other ways to support if they have to move away. Do you know anyone in a different part of the country who could put them up for a few weeks? Can they sell stuff on Vinted? Can you loan them your car?
Good luck. It's tough out there but just emphasise to them it's not them, it's the situation and they just need to keep trying.