feature: monitor categories

**Is your feature request related to a problem? Please describe.**
No

**Describe the solution you'd like**
Add support for monitor categories (like in Uptime Kuma or Better Stack) and ensure these categories are also reflected and carried over to status pages, so status pages can group and display monitors based on their assigned categories.

**Additional context**

No files, tests, or entry points are named. Start by mapping how monitors are stored and rendered on status pages, then define category assignment, persistence, and grouping requirements; done means categories appear consistently for monitors and on their associated status pages.

Written by the indexing model from the issue text.