feat(api): create unified API server with first 3 modules

New consolidated Hono/Bun API server at apps/api/ that replaces individual
app servers. One process, one port, one auth middleware, one container.

Modules ported:
- calendar: RRULE expansion, ICS import, Google Calendar (stub)
- contacts: avatar upload (S3), vCard import/parsing
- mukke: audio upload/download presigned URLs, batch cover art

Architecture: each module registers routes under /api/v1/{module}/*
using the shared-hono middleware stack (auth, rate limit, error handler).

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/api/tsconfig.json

@@ -0,0 +1,14 @@
+{
+	"compilerOptions": {
+		"target": "ESNext",
+		"module": "ESNext",
+		"moduleResolution": "bundler",
+		"strict": true,
+		"esModuleInterop": true,
+		"skipLibCheck": true,
+		"outDir": "dist",
+		"rootDir": "src",
+		"types": ["bun-types"]
+	},
+	"include": ["src/**/*.ts"]
+}