I did move from physics to becoming a SWE. I could put the knowledge I gained doing 3D rendering and GPU compute used for visualization and simulations in my academic jobs on my CV, and get a job as a SWE that way. Later I moved to another job where I could use my physics background to help develop a new sensor.

As for how to market yourself: first you should convert your academic CV to one that is suited for the type of companies you are applying for. Unless you wrote something that ended up in Nature or some other super high profile journal, companies typically don't care about your publications. What they do care about is things like: can you communicate well? How well can you organize things on your own? Do you handle stress well? You did a PhD, so the answer to those things is yes, you just need to write that in your CV in a way a company recruiter/interviewer understands, even if they themselves are not from academia. So you don't have two halves that belong to different resumes, you are just one person and you just translate your resume to the "language" that your prospective job provider speaks.

Finally, your list of skills does not need to be a perfect match for what a company is looking for. Of course, there needs to be some overlap, but as long as it means you can pick up new things quickly, it will be fine. That and being a good fit for the company's culture are the most important things.

I did not start out with a unicorn role, but in I found ways to apply my physics background in my current job.