Add clients in front of broadcasts

[slmnio]

It would be nice to have a personal key that producers can use instead of renaming all of their OBS browser sources.
Instead of using /broadcast/st4/ingame, a producer could use /client/slmn/ingame which ties to a Client record on the SLMN.GG Airtable. The broadcast can then be set and updated there.

[slmnio]

This commit adds clients in a way that matches the broadcasts pages. To maintain backwards compatibility (and because there's good reasons to keep a dedicated /broadcast/ URL), you can still access all broadcast overlays with /broadcast/.

You can migrate to a client-based solution by changing /broadcast/{key}/{page} to /client/{clientKey}/{page}. For example, /broadcast/st4/break to /client/slmn/break. You can create or update clients in the Clients tab of Airtable.