EPIC#3: Generating a free room in between classes

# What
Offer users the opportunity to find a free room (to study in, etc) and integrate it into their Notangles timetable as a single source of truth.

# Why
Useful feature to improve quality of life and reduce time users need to take to find a free room, improve productivity and convenience.

# Brief Implementation Details

- Frontend will mainly be reusing components
- Backend will involve creating GraphQL queries

Start by tracing the existing timetable UI and the backend's GraphQL query entry points; the issue does not name files or tests. Confirm the room-availability data and integration workflow with maintainers before implementation. Done means users can find a free room and add it to the timetable as a single source of truth, with coverage for the new behavior.

Written by the indexing model from the issue text.