Migrate room filtering to backend search API

[Yalilix]

What

Migrated room filtering from client-side logic to the existing backend room search API.

This PR adds a LiveFilterRoomLoader service that builds a filtered GET request to /api/rooms/search, decodes the returned room map, and extracts the matching room IDs for the app to use when displaying filtered room results.

Why

The app previously relied on filtering room data on-device, which duplicated logic that already exists in the backend and could become inefficient as the room dataset grows.

Using the backend search endpoint keeps the mobile app aligned with the established API behaviour and avoids maintaining complex filtering logic on the client.

How

• Added a filter room loader service for fetching filtered room IDs from the backend.
• Constructed the search URL using query parameters such as datetime, buildingId, capacity, duration, usage, location, startTime, and endTime.
• Decoded the backend response as a room ID to room details map.
• Extracted the dictionary keys as the filtered room IDs.
• Added test doubles and unit tests for successful decoding, query parameter construction, nil filter handling, and failure behaviour.

Key checks:

• 🚩Attached screenshot or recording of the changes in related tickets
• Code comments where needed
• No new warnings

Automated tests:

• 🚩Unit tests added

Manual tests:

• Big iPhone (iPhone 17 Pro Max)
• Small iPhone (iPhone SE)

Screenshot / Recording

N/A

[xleonx0x]

lgtm, just fix those small things e

[xleonx0x]

name doesn't match file