One of the Perl language servers, PLS, offers this capability to some extent. This should work with all editors/IDEs with language server support, in particular with VSCode.

In Emacs with lsp-mode, it shows the first line of the perldoc entry, in your example SHORT EXPLANATION IN ONE-LINE, in the minibuffer (as Eldoc usually does). This works for builtin functions and predefined variables, but is pretty useless for modules where the first line of the perldoc entry usually is the constant heading NAME.

PLS also offers the whole perldoc entry (markdown formatted) on request (in Emacs: M-x lsp-describe-thing-at-point). I am not too enthusiastic about this feature because hyperlinks in the perldoc text are resolved against https://metacpan.org/ which means you might not get the documentation which matches your installed version. Also, it doesn't work for modules in your current workspace.

The other Perl language servers either don't support hover or use it for different things - the specification does not clearly specify what should happen on hover. Caveat Emptor.