Ask HN: Courses/textbook recommendations for studying statistics and proofs?

Hi HN, as the title suggests I want to learn a more rigorous treatment of statistics including the proofs that go along with it.

I have a masters in a STEM subject so I am familiar with plug-and-chug mathematics up to things like Laplace transforms, fourier transforms, basic PDE's with straightforward solutions and trivial boundary conditions (plug and chug!)

But I lack the 'mathematical maturity' for proof based approaches.

Can anyone recommend a book/course for a first course in statistics?

And a second+ course (perhaps a different book/books)?

Ideally I would like to cover all of the common undergrad topics, from proofs, figuring out means and medians, up to things like bayesian statistics, and things like design of experiments.

As an aside I'm also incredibly interested in Ryan O'donnell's CS Theory Toolkit[1] @CMU but again I am missing the prerequisite comfort in proof based math for that, so any resources on that would also be appreciated (I think this counts towards the topic title of 'and proofs' ;) )

[1] https://www.youtube.com/watch?v=prI35GmCon4&list=PLm3J0oaFux3ZYpFLwwrlv_EHH9wtH6pnX