If you’re looking for a textbook, when I was re-learning stats a few years back I found Box & Hunter’s Statistics for Experimenters to be fantastic.
Disclaimer - I transitioned to PM from engineering and work on hardware & matsci products, so my experience might not be representative. But, I felt it was approachable and I recommend it to anyone who wants to build a rock-solid foundation, at least up to the hypothesis testing chapters. Past that you get into ANOVA and designed experiments, which is interesting but probably overkill.
https://www.amazon.com/Statistics-Experimenters-Design-Innovation-Discovery/dp/0471718130 One of the books every engineer should read!
> I'm missing some pre-requisites like probability theory and statistical inference.
For your background, the traditional texts are:
I'm in a M.S. Statistics program. The only overlap you would have in a statistician + engineering role would be P and MLC, maybe some C, in a topic called "survival analysis" (or, as it is called in engineering, "reliability"). Survival analysis is not covered to the depth where you need it for engineering the way it is taught in P and MLC. What would be an extreme deficiency is a lack of a background in experimental design, which is what distinguishes a statistician from most other roles (actuary, data analyst, etc.). I would recommend that you read Statistics for Experimenters: Design, Innovation, and Discovery by Box, Hunter, and Hunter, which is specifically geared toward engineers and other "hard sciences" which don't have a lot of math exposure (relative to a math major or statistician).