There is not enough information in pasted code for a language server to indent pasted in python code. Try copy pasting a random stackoverflow snippet into deeply indented python code.

Why would you need a language server for that? You simply prepend the indentation of the current line to every line of the pasted text.

Do you know of a IDE that does this automagically?

I use Neovim with the yanky plugin.

https://github.com/gbprod/yanky.nvim