But what is a <$>? Should one google something like that and hope that Google honors it like a word instead of ignoring it like it usually does punctuation?

No... that's what Hoogle is for. You can literally search by symbol or by type signature, and it's amazing.

Examples

- By symbol: https://hoogle.haskell.org/?hoogle=%3C%26%3E

- By signature: https://hoogle.haskell.org/?hoogle=Functor%20f%20%3D%3E%20f%...