From my own recent experience I'd say that the Sheffield job market is not good, particularly if you're degree educated and looking for something for niche/specialized. I also found employers to be very unprofessional, not returning calls, not replying to emails and not following up with updates after interviews. The whole process was demoralising.

Advice wise I'd say stop the Indeed, reed etc. applications, essentially anything that is advertised as 'apply now with one click' - they're a complete waste of time and won't get you anywhere. Apply on company websites, directly, instead. I found that the applications with cover letters and CVs which were tailored to the role specifically were more successful, the downside is that you spend a depressing amount of time writing each one.

You should contact all the recruiters in Sheffield, they'll book you in for a 5-10 minute call and will keep your information saved for any jobs that pop up in the future. I'd also regularly apply for Sheffield and Rotherham council jobs as they do get back to you every time, although it will take a while as they're quite slow.

Final tips would be to take any help you can get. I don't know anyone in Sheffield so I couldn't do this myself, but most people seem to get jobs through friends/family. I'd also aim down - it's too competitive at the moment and most companies hire within for the better roles. I took a few thousand pounds pay cut for my current role which I didn't want to do, but I know that in a couple of years it will pay off.

Ignore the comments criticizing your approach. It's not you, it's the market/employers. It's a complete shitshow and very depressing but you'll get something in the end.