Improve the UX of the "Request bridges" flow

Following recent improvements to the built-in bridges (#41617 (closed)) and provide a bridge dialogs (#40552 (closed)), we should also take a look at improving the UX of the request a bridge dialog. However it makes sense to wait on the outcome of tpo/anti-censorship/rdsys#49 (closed) first, where the Anti-Censorship team will be considering a new CAPTCHA strategy.