1. Should I stay in recruitment now or move back home and focus on job applications? I feel like if I stay longer I’ve sold myself to this career I don’t like
If you want to change careers, then now would have been a good time to do so.
On the other hand...
2. How can I improve my odds of getting a job in consulting or the civil service?
You work in recruitment and you don't know the answer to this question? If you leave now, what makes you think your odds will suddenly improve?
If you're in a priviledged situation where you get to learn what is required to get a job in consulting or the civil service, don't you think you should look into this first before quitting? I recommend doing your research in these areas first (or at least ask your colleagues working in these sectors) before moving on.