Career shift advice into Game Dev

Hey All!

As per title, I am thinking of moving into the gaming industry (Been an avid consumer for a while now), but not sure how my past experience fits best, or at all.

About my background, I have a master's in AI, a few years as an IT solutions architect and solo-founded several SaaS products, handling everything from market research and product development to sales and delivery.

I feel one of my key strengths is in Product Management—particularly the balance between vision, business , people, and technical. I'd love to "own" a game in a similar way to how one manages a software product: guiding it through iterative development cycles to make it the best it can be. The added benefits over the traditional Saas is for me the artistic creativity, making it an intersection of so many fields I partake in.

However, to my knowledge that's not a common title in Game Dev. Is Producer the equivalent?

I know the Game Dev industry can be hard, lots of passionate among us. So what kind of position would you recommend to me, and if I can't access them now because of my lack of work experience in it, what kind of pathway would you advice?

I really appreciate any insights you can share!