🐛 fix: resolve tsconfig issues across all NestJS backends

Define compiler options locally instead of extending shared-tsconfig
to fix drizzle-orm type compatibility issues. Also add missing
shared-vite-config dependency to skilltree/web.

Fixed backends:
- calendar, chat, clock, contacts, nutriphi
- picture, presi, questions, skilltree, todo

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

apps/clock/apps/backend/tsconfig.json

@@ -1,3 +1,27 @@
 {
-	"extends": "@manacore/shared-tsconfig/nestjs"
+	"compilerOptions": {
+		"target": "ES2021",
+		"module": "commonjs",
+		"moduleResolution": "node",
+		"declaration": true,
+		"removeComments": true,
+		"emitDecoratorMetadata": true,
+		"experimentalDecorators": true,
+		"allowSyntheticDefaultImports": true,
+		"outDir": "./dist",
+		"baseUrl": "./",
+		"rootDir": "./src",
+		"incremental": true,
+		"skipLibCheck": true,
+		"strictNullChecks": true,
+		"noImplicitAny": true,
+		"strictBindCallApply": true,
+		"forceConsistentCasingInFileNames": true,
+		"noFallthroughCasesInSwitch": true,
+		"esModuleInterop": true,
+		"resolveJsonModule": true,
+		"sourceMap": true
+	},
+	"include": ["src/**/*"],
+	"exclude": ["node_modules", "dist"]
 }