Design backlog: Change drop-down menus in Reporting to match in admin/reg

#### Describe the task

Incorporate the drop-down menu functionality (ability to type and live filter) from registration and the administrative area to the reporting module, which currently only filters with the first letter.

#### Acceptance Criteria

- [ ] first
- [ ] second
- [ ] third

#### Definition of Done

- [ ] first
- [ ] second
- [ ] third

#### Additional context

- Add any other context about the task here.
- Or here

Start by comparing the drop-down behavior in the registration and administrative areas with the reporting module, which currently filters only by the first letter. Identify the reporting entry points and confirm which menus need the same type-to-filter behavior. Done means reporting menus support typing and live filtering, with the acceptance and definition-of-done checks replaced by concrete results.

Written by the indexing model from the issue text.