refactor: rename web/ to api/ to better reflect its purpose

The web/ folder contains the REST API, WebSocket server, and OAuth
routes — not a web frontend. Renaming to api/ clarifies this distinction
since the actual web frontend lives in panel/.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

api/tsconfig.json

@@ -0,0 +1,38 @@
+{
+  "compilerOptions": {
+    // Environment setup & latest features
+    "lib": ["ESNext"],
+    "target": "ESNext",
+    "module": "Preserve",
+    "moduleDetection": "force",
+    "allowJs": true,
+    // Bundler mode
+    "moduleResolution": "bundler",
+    "allowImportingTsExtensions": true,
+    "verbatimModuleSyntax": true,
+    "noEmit": true,
+    // Best practices
+    "strict": true,
+    "skipLibCheck": true,
+    "noFallthroughCasesInSwitch": true,
+    "noUncheckedIndexedAccess": true,
+    "noImplicitOverride": true,
+    "baseUrl": ".",
+    "paths": {
+      "@/*": [
+        "./src/*"
+      ],
+      "@shared/*": [
+        "../shared/*"
+      ],
+      "@bot/*": [
+        "../bot/*"
+      ]
+    },
+    // Some stricter flags (disabled by default)
+    "noUnusedLocals": false,
+    "noUnusedParameters": false,
+    "noPropertyAccessFromIndexSignature": false
+  },
+  "exclude": ["node_modules"]
+}