[Gantt Chart] - 1.2.1 Audit frontend filter and design new API

Description

Currently, filtering on the Gantt chat is entirely on the frontend. All project/work package/task data is loaded up front, and filters (team, car, etc.) just hide/show elements client-side. This is part of why initial page load is so slow.
This ticket has two parts: document how filtering currently works so we know exactly what needs replacing, and design the shape of the new backend API that only returns data matching active filters, so #4467 has a clearer spec.
Note: no code changes for this ticket! Investigation and design only

Acceptance Criteria

• Written documentation (a doc, or a detailed comment on this ticket) listing every filter currently available
• For each filter, write how it's currently implemented: what data is fetched, and what frontend logic hides/shows elements based on the filter
• Proposed API design
  -- What endpoint(s) the frontend will call when a filter changes (i.e. one endpoint with query params vs. separate endpoints per filter type)
  -- What query parameters it accepts
  -- What shape of data it returns (which fields, whether it's the same shape as current frontend data or different)
  -- How multiple simultaneous filters combine

Proposed Solution

• Find filters in frontend code
• Trace how filter selection currently works
• List all filter types
• Decide on one endpoint vs multiple, how filter values are sent, whether multiple values can be selected for a filer and how that's represented, what happens when a filter matches nothing, etc.

Mocks

No response

Start by locating the Gantt Chart frontend filter implementation and tracing how filter selections fetch data and hide or show elements. Document every available filter and its current data flow, then record the proposed endpoint, parameters, response shape, and combined-filter behavior; completion is the documented investigation and API design with no code changes.