What positions in industry should I apply for after a phd and postdoc in software engineering?
We don't know if you will get one of the jobs that requires 3-5 years experience.  But there's no reason not to try.

As you're reading job descriptions, avoid the ones that clearly involving sitting and coding for eight hours a day -- because you say that's not your strong suit.

When you apply for a job you think you would be good at, you must tailor your CV, your cover letter, and your interview to the specific job.  Piece together the work you've done to make a jigsaw puzzle picture that resembles, to a reasonable extent, the picture they have in mind.  This does require some chutzpah.  That's okay.  The job hunt process is not the place for humility.

In other words, you will argue that you have 3-5 years' relevant experience (in some sort of equivalent form).

If that doesn't get anywhere -- then you can go back to the drawing board.

(By the way, you might want to get involved with a headhunter.  I myself can't advise for or against going that route.)