When I post a mastodon link elsehwere (e.g., in an email signature), which should I use? Why?
Honestly, this. Adding https to the text is just aesthetically unnecessary. However, you would want to keep the https functionality, so keep it in the actual link.
Tldr; each has different use-cases.
Try typing "/@peterdrake@qoto.org/" into your browser (without the quote-slashes) and you will have your answer.
@peterdrake I display the username and server because it denotes what I go by and which federated instance I’m on, but I link it to full URL because that’s the proper link and destination for my profile page.