This is an option that seems to be disabled by default.
To enable (in VS 2019):
-
Go to
Tools -> Options -
type copy in the search box
-
Under
Text Editor -> Advanced… -
Check Copy rich text on copy/cut

Top copy as formatted
Once the feature is enabled, depending on the target, this may be a two-step process. If, after copying and pasting code, it still appears as unformatted (e.g. if pasting into a web browser), use the approach suggested by marcus, by first pasting into wordpad.exe (start -> run -> type wordpad), then copying the text from within Wordpad again, and pasting into the target application/browser.