…Reading basic PM books like the Startup Owners Manual is a good start. For the interview, I think reading a lot of technical strategies makes you flexible and this interview book helped prepare for the specific questions companies will throw at you.
I would take a look at the specific job postings and understand where your gaps are at. A lot of the Amazon PM roles look for prior experience as a PM. I came in through an MBA program so they were able to be a little more flexible with my background and teach me what I needed to know to be a good PM.
I would refer to a previous comment I made about getting real experience as a PM (even if it is as a part-time intern at a small startup). When you get an Amazon interview, see if you can come up with experiences you have had that hit their Leadership Principles.
…I do some version of that [create a product prototype (even if its in PPT) but walk through the “work”] in interviews when I can or follow up after the interview with something more thought out as you described. I have also coded out my own website using Python and deployed it from Digital Ocean (which is great to talk about). I have a few posts I have put on Medium and LinkedIn. I think the more you can bring the interviewer in, and show them how you are unique and a value add to their company beyond just a resume, the better.