Best way to learn modern Physics?

You can't really skip anything. Concepts and techniques recur, over and over again. Half of dealing with the "advanced" stuff is just taking its leading order term and pretending it's classical. Quantum electrodynamics is fun for explaining atomic physics and below, but for everything bigger than a molecule it's useless and classical E&M rules the day.

So... yeah, you've got to start at the beginning. Or at least, know what you're passing by.

Everyone learns differently, so you are going to get a lot of different types of suggestions. I learned physics through a mix of the standard academic route and some autodidactic explorations, so I'm not particularly married to the idea of learning things 'in the proper order'. On the other hand, I've experienced what it is like to learn a part of something but to have a hole in your knowledge because you learned it out of the expected order. Filling those holes is helpful, but just because you skipped something doesn't mean you can't learn it later.

I would suggest to pick up a used copy of Modern Physics by Serway Moses and Moyer. You should be able to find an old edition for about $20. Read through it once first, don't try to work the problems, just absorb the concepts. This will give you a basic map of the idea space, so you know what you'll need to learn. Then find a part which you find fascinating and try some of the problems. You'll likely find you'll be missing some tools and then you'll need to go back and learn some things, but at least you will know what you need it for, and your interest will fuel your ability to work through the problems.

You need those cores of mechanics, E&M, and QM. They're so important that most physics majors take them twice, first at an introductory level and then at a more detailed level.

It's only a slight exaggeration to say that the simple harmonic oscillator is the most important model in physics. You learn it in freshman mechanics, and you still need it to understand quantum field theory.

The hard part is that to really understand physics, you need to work through problems. Reading or lectures alone won't do it. You'll need to learn to apply the concepts from what you're learning. If you are following textbooks, definitely work through the problems.

(my credentials for this advice are that I have a PhD in physics)

You do want that basis of classical mechanics, because one of the things it teaches you is how to observe a phenomenon and think about the interactions taking place, building up that intuition you're lacking. Physics requires more than just memorising formulas and pattern-matching. It requires you to properly think about what's going on in the interaction you're looking at.

I’d recommend So You Want to Learn Physics… by Susan Rigetti: https://www.susanrigetti.com/physics

This could serve your purpose: https://www.goodtheorist.science/ .