I feel many comments here are confusing "Product" Management with "Project" Management. Many describing being a "people person" which isn't (in my eyes) a needed trait for a product manager, but is for a project manager. There are obviously social aspects of being a product manager, but much of it has to do with relaying what's in your head moreso than trying to manage people day-to-day.
To me, what matters for the OP, is that you are actually a product person? In my experience too many people are just terrible at understanding their field, products, how to actually break down product problems to their basic pieces and build solutions up from there. Being able to trust their designers, ui/ux, engineers to take their vision and execute (or simply just being good at transferring the vision in their head to being executable by others.
If you're not great at the above, please don't try and shoehorn yourself into product management. I've had too many terrible product managers that should have been something entirely different in my day that just literally ruins years of people's lives.
If you are not interested / good at the above, I'd consider a more Project Management role, which is about figuring out how to take a team and turn them into a well-oiled machine that loves working together towards common goals.
In many places (like startups) the line between the two above obviously blurs, my only concern is moving into Product Management role that you're not fit for. I say this more in general for people thinking about this themselves - mostly because of all the Product / Project Managers I've seen, I'd say 2/10 of them I'd actually want to work with again (though they both had engineering backgrounds which works in your favor).