Publish contest bot cast *after* contest projection created

[rbennettcw]

Link to Issue

Closes: #10922

Description of Changes

• Previously, the contest bot cast was published before the contest projection was created, so the end date of the contest wasn't available to render. This change invokes the cast publish after the projection is created, so that the end date will be available.

Test Plan

• Ask contest bot (for whatever environment you're using) to create a contest
• After a few seconds, the bot should reply with the contest frame– confirm that it shows the end date

Deployment Plan

N/A

Other Considerations

N/A