I don't know about Claude, but when it comes to LaTeX IDE, I will always recommend TeXStudio over everything else. It handles all the annoying problems of LaTeX setup and compilation, and it provides a discoverable interface with classic-style menus (words, it has words instead of inexplicable little icons!) for various common tasks.

I say that as someone who uses a tricked-out Vim for my own LaTeX workflow, and VS Code for several programming languages.