I don't have any great recommendations and unfortunately my advice may be not what you want to hear. What I tell my students is "You don't need to know math to build good models, but you need to know math to know why your models are wrong." But this is even a contentious statement within the community. (Personally I'm more interested in exploring what we can build and understand rather than focusing on throwing more compute and data at problems. There's a lot of work to be done that does not require significant compute, but it isn't flashy and you'll get little fame. Every famous model you know has some unsung hero(s) who built the foundation before compute was thrown at the problem). I was previously a physicist and we similarly frequently express that you do not know the material unless you can do the math. Physicists are trained in generating analogies as they help communication but this sometimes leads to people convincing themselves that they understand things far more than they actually do. They say the devil is in the details, and boy are there a lot of details. (Of the science communicators, I'm happy those are the ones you mention though!) But do not take this as gatekeeping! These groups are often happy to help with the math and recommend readings. ML is kinda a while west and you can honestly pick a subdomain of math and probably find it useful, but I would start by making sure you have a foundation in multivariate calculus and linear algebra.

As to paper reading, my suggestion is to just start. This is a fear I faced when I began grad school and it feels overwhelming and like everyone is leagues ahead of you and you have no idea where to begin. I promise that is not the case. Start anywhere, it is okay, as where you end up will not matter too much on where you begin. Mentors help, but they aren't necessary if you have dedication. As you read you will become accustomed to the language and start to understand the "lore." I highly suggest following topics you find interesting backwards through time, as this has been one of the most beneficial practices in my learning. I still find revisiting some old works reveals many hidden gems that were forgotten. Plus, they'll be easier to read! Yes, you will have to reread many of those works later, as you mature your knowledge, but that is not a bad thing. You will come with newer eyes. Your goal should be to first understand the motivation/lore, so do not worry if you do not understand all the details. You will learn a lot through immersion. It is perfectly okay if you barely understand a work when first starting because a mistake many people make (including a lot of researchers!) is that a paper is not and cannot be self contained. You cannot truthfully read a work without understanding its history and that only comes with time and experience. Never forget this aspect; it is all too easy to deceive yourself that things are simpler than they are (the curse of hindsight).

I'd also suggest to just get building. To learn physics you must do physics problems. To learn ML you must build ML systems. There are no shortcuts but progress is faster than it looks. There's hundreds of tutorials out there and most are absolute garbage but I also don't have something I can point to that's comprehensive. Just keep in mind that you're always learning and so are the people writing tutorials. I'm going to kinda just dump some links, they aren't in any particular order sorry haha. Its far from comprehensive, but this should help you getting started, nothing in here is too advanced. If it looks complicated, spend more time, you'll get it. It's normal if it doesn't click right away and there's nothing wrong with that.

https://www.youtube.com/@Mutual_Information

https://www.youtube.com/@EmergentGarden

https://www.youtube.com/@pascalpoupart3507

https://www.youtube.com/@AndrejKarpathy

https://www.youtube.com/@alfcnz

https://www.youtube.com/@rmcelreath

http://neuralnetworksanddeeplearning.com/

https://adversarial-ml-tutorial.org/introduction/

https://www.deeplearningbook.org/

https://nlp.seas.harvard.edu/2018/04/03/attention.html

https://huggingface.co/blog/annotated-diffusion

https://lilianweng.github.io

https://pytorch.org/ecosystem/

https://medium.com/pytorch/archive

https://www.inference.vc/