OP specifically said the aren't pursuing a career in physics and that they are just interested in learning some physics for personal interest - what's the point of scaring interested people with a list of math topics that are useful at the graduate level? Do you realize not everyone wants to get to a graduate level, and if they do they still need to start from the basics?
You can have a decent understanding of classical mechanics without ever needing functional analysis or complex analysis or PDEs and yes, you can even do without differential geometry. Yes, even the Lagrangian and Hamiltonian approaches. Goldstein barely mentions differential geometry for most of the book.
I already discussed similar things with you once with another account, back then you also jumped immediately to "maybe you're American so you had a lesser education". For what it's worth, I come from a renowned European German speaking university, and I'm on the theoretical side, but I think that's beside the point.
If the question was "I want to apply to PhDs in high energy theory, what math should I study" then I'd agree with your list, but I don't agree with it for the question of OP.