I should say, for the avoidance of doubt, despite my negative tone: I think you’re in a good position, Product Management has a low bar for transitioning — and greatly benefits from soft skills — and so as long as you’re in the right organisation, with a good product culture, you’ll be able to progress your career very quickly.
The downside of the low bar for transitioning is that struggling companies will shoe-horn anyone who expresses an interest into Product Management and they’ll really, really struggle. A software engineer in a struggling company can live in relative ignorance, not so for a product manager, a product manager’s ability to work effectively is dependent upon the company functioning effectively.
If you can get into a good product company, in any role, you’ll be on the right track!