Engineering: keep puzzle tracker accurate from chat commands

Engineers marking puzzles solved in chat let status drift, causing missed handoffs. This updates trackers and posts channel notices so organizers see accurate status and begin follow-ups.

Overview

Unrecorded puzzle solves create status drift and force manual follow-ups for organizers. This flow turns an engineer's in-chat solve command into an updated tracker record and channel broadcasts, eliminating missed handoffs and giving organizers accurate status so follow-ups begin quickly.

Notable Features

Update puzzle tracker records
Broadcast solved messages to channels
Log solver name and metadata