PhD and postdoc with no first author publications- realistically what are my career prospects?
Are you intending to stay in academia? You stated in your question that you've always wanted to be a "researcher"... you should be aware that there are many industry positions with similar duties and responsibilities. Having zero publications isn't good, but your skills as a researcher aren't limited to the length of your CV. I would spend some time investigating positions in industry that would allow you to perform similar work to what you're doing now in academia.

Hopefully someone else can post something focusing more on your academic prospects.



Edit: Your comment of "not sure if my work is relevant to industry" deserves more attention that an answer on an online forum can provide, but very briefly:

You are not defined by your field. I have a BS in psychology, a PhD in biomedical engineering (which actually was entirely neuroscience, but all my courses were electrical engineering), my first two jobs were a bank quantitive  analyst and a data science manager for an insurance company, and I now work for a cybersecurity research firm. When writing a resume you choose which skills to highlight and how to sell yourself. I strongly recommend you re-evaluate your own skill set and see whats out there that interests you.