refactor: wave 1 - extract leaf modules, rename catch-all files, split index.ts hooks

- Split 25+ index.ts files into hook.ts + extracted modules
- Rename all catch-all utils.ts/helpers.ts to domain-specific names
- Split src/tools/lsp/ into ~15 focused modules
- Split src/tools/delegate-task/ into ~18 focused modules
- Separate shared types from implementation
- 155 files changed, 60+ new files created
- All typecheck clean, 61 tests pass

src/tools/delegate-task/model-string-parser.ts

@@ -0,0 +1,10 @@
+/**
+ * Parse a model string in "provider/model" format.
+ */
+export function parseModelString(model: string): { providerID: string; modelID: string } | undefined {
+  const parts = model.split("/")
+  if (parts.length >= 2) {
+    return { providerID: parts[0], modelID: parts.slice(1).join("/") }
+  }
+  return undefined
+}