Improve library team mention message for consistency

[yaahc]

Further continuations upon rust-lang/rust#95986.

I reviewed the output after the previous change to add the to_mention message for libs and wasn't thrilled with the output. It seemed to duplicate the welcome message that highfive posts generally as well as being very information dense. I've tried to reorder how we present information and reframe it so it flows well with the subsequent welcome message.

I tried reordering it all together so the welcome message comes first, but it appears that the self.set_assignee function needs to be called first before self.is_new_contributor or else some of the state within the Handler ends up being a python dict instead of the expected JSON... Didn't feel like debugging or refactoring that, but I think I've arrived upon a wording that looks good even if it comes first. Also this way I don't necessarily mess up other team's welcome messages that may already be optimal if placed first.

[yaahc]

(fake) r? @Mark-Simulacrum