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/interactive-bash/tmux-path-resolver.ts

@@ -0,0 +1,71 @@
+import { spawn } from "bun"
+
+let tmuxPath: string | null = null
+let initPromise: Promise<string | null> | null = null
+
+async function findTmuxPath(): Promise<string | null> {
+  const isWindows = process.platform === "win32"
+  const cmd = isWindows ? "where" : "which"
+
+  try {
+    const proc = spawn([cmd, "tmux"], {
+      stdout: "pipe",
+      stderr: "pipe",
+    })
+
+    const exitCode = await proc.exited
+    if (exitCode !== 0) {
+      return null
+    }
+
+    const stdout = await new Response(proc.stdout).text()
+    const path = stdout.trim().split("\n")[0]
+
+    if (!path) {
+      return null
+    }
+
+    const verifyProc = spawn([path, "-V"], {
+      stdout: "pipe",
+      stderr: "pipe",
+    })
+
+    const verifyExitCode = await verifyProc.exited
+    if (verifyExitCode !== 0) {
+      return null
+    }
+
+    return path
+  } catch {
+    return null
+  }
+}
+
+export async function getTmuxPath(): Promise<string | null> {
+  if (tmuxPath !== null) {
+    return tmuxPath
+  }
+
+  if (initPromise) {
+    return initPromise
+  }
+
+  initPromise = (async () => {
+    const path = await findTmuxPath()
+    tmuxPath = path
+    return path
+  })()
+
+  return initPromise
+}
+
+export function getCachedTmuxPath(): string | null {
+  return tmuxPath
+}
+
+export function startBackgroundCheck(): void {
+  if (!initPromise) {
+    initPromise = getTmuxPath()
+    initPromise.catch(() => {})
+  }
+}