refactor: use DI-ed cached FeaturesRepository in flags router (calcom#27394)

## What does this PR do?

Replaces direct instantiation of `FeaturesRepository` with the dependency-injected version using `getFeaturesRepository()` from the DI container in the feature flags router.

**Key improvement:** The DI-ed version uses Redis caching, replacing the previous in-memory 5-minute cache implementation which was not ideal. This follows the established DI pattern in the codebase for loose coupling, better testability, and more robust caching across instances.

## Type of change

- [x] Refactor (non-breaking change that improves code quality)

## Mandatory Tasks (DO NOT REMOVE)

- [x] I have self-reviewed the code (A decent size PR without self-review might be rejected).
- [x] I have updated the developer docs in /docs if this PR makes changes that would require a [documentation change](https://cal.com/docs). N/A - no documentation changes needed.
- [x] I confirm automated tests are in place that prove my fix is effective or that my feature works.

## How should this be tested?

1. Verify feature flags functionality works as expected:
   - Feature flag list endpoint should return all features
   - Team feature check should work correctly
2. No environment variables needed beyond standard setup

## Checklist

- [x] My code follows the style guidelines of this project
- [x] I have checked if my changes generate no new warnings

## Human Review Checklist

- [ ] Verify `getFeaturesRepository()` returns a properly configured instance from the DI container
- [ ] Confirm the DI container properly injects the Prisma client
- [ ] Verify Redis caching is working as expected for feature flag data

---

**Link to Devin run:** https://app.devin.ai/sessions/2ff6e4551c8649e4b6178b31a2195327
**Requested by:** @eunjae-lee

Author: eunjae-lee

packages/features/flags/server/router.ts

@@ -1,16 +1,13 @@
-import { z } from "zod";
-
+import { getFeaturesRepository } from "@calcom/features/di/containers/FeaturesRepository";
 import type { AppFlags } from "@calcom/features/flags/config";
-import { FeaturesRepository } from "@calcom/features/flags/features.repository";
-import { prisma } from "@calcom/prisma";
 import publicProcedure from "@calcom/trpc/server/procedures/publicProcedure";
 import { router } from "@calcom/trpc/server/trpc";
-
+import { z } from "zod";
 import { map } from "./procedures/map";
 
 export const featureFlagRouter = router({
   list: publicProcedure.query(async () => {
-    const featuresRepository = new FeaturesRepository(prisma);
+    const featuresRepository = getFeaturesRepository();
     return featuresRepository.getAllFeatures();
   }),
   checkTeamFeature: publicProcedure
@@ -21,7 +18,7 @@ export const featureFlagRouter = router({
       })
     )
     .query(async ({ input }) => {
-      const featuresRepository = new FeaturesRepository(prisma);
+      const featuresRepository = getFeaturesRepository();
       return featuresRepository.checkIfTeamHasFeature(input.teamId, input.feature as keyof AppFlags);
     }),
   map,