Discord Ticker

Almost forgot about this. This is a feature not critical to the functionality of the whole tool, but something I would really like to have implemented after everything else works (asap if possible). The old form used a (relatively simple?) webhook, no bot required for now.

You have probably already seen the Discord ticker-channels we had for past events, but I'll outline what it's supposed to do.
In the public channel:
- announce when a new run gets submitted, only including the basic information (runner, game, category, platform)
- announce when a run gets accepted/rejected/passes a round of cuts, basic information
Screenshots:

In the private channel:
- announce when a new run gets submitted, complete info
- announce when team invites are accepted/rejected, basic info
- announce when a run gets edited and by who, only include the info that has been changed
- announce when a run gets removed/accepted/rejected/passes a round of cuts and by who, basic information
Screenshots:

No files, tests, or entry points are named. Start by tracing where runs and team-invite status changes are handled, then identify the existing webhook integration point; done means the listed public and private Discord announcements are emitted with the specified level of detail for each event.

Written by the indexing model from the issue text.