feat(v0.3): M6 — new tab opens in the active tab's directory

- title-util.cwdFromOsc7: parse cwd from OSC 7 (file:// URL); 4 unit tests
- terminal-session: register OSC 7 handler → cwd getter; opts.cwd → sent in the
  attach frame on a fresh session
- protocol/types: ClientMessage attach.cwd (absolute path); validated
- session/manager/server: thread cwd → createSession spawn cwd (defaults homeDir)
- tabs: '+' (newTab) opens in the active tab's reported cwd, falls back to home
- Verified: server attach.cwd spawns there; cd /private/tmp → + → new tab pwd is
  /private/tmp. 212 tests green.

src/protocol.ts

@@ -133,8 +133,21 @@ function validateAttach(obj: Record<string, unknown>): ParseResult {
     return { ok: false, error: 'attach.sessionId field is required' }
   }
 
+  // Optional cwd (M6): must be an absolute path string if present.
+  const rawCwd = obj['cwd']
+  let cwd: string | undefined
+  if (rawCwd !== undefined) {
+    if (typeof rawCwd !== 'string' || !rawCwd.startsWith('/')) {
+      return { ok: false, error: 'attach.cwd must be an absolute path string' }
+    }
+    cwd = rawCwd
+  }
+
   if (sessionId === null) {
-    return { ok: true, message: { type: 'attach', sessionId: null } }
+    return {
+      ok: true,
+      message: cwd !== undefined ? { type: 'attach', sessionId: null, cwd } : { type: 'attach', sessionId: null },
+    }
   }
 
   if (typeof sessionId !== 'string') {
@@ -151,7 +164,10 @@ function validateAttach(obj: Record<string, unknown>): ParseResult {
     }
   }
 
-  return { ok: true, message: { type: 'attach', sessionId } }
+  return {
+    ok: true,
+    message: cwd !== undefined ? { type: 'attach', sessionId, cwd } : { type: 'attach', sessionId },
+  }
 }
 
 // ─── serialize ────────────────────────────────────────────────────────────────

src/server.ts

@@ -229,7 +229,7 @@ export function startServer(cfg: Config): { close(): Promise<void> } {
 
         let session
         try {
-          session = manager.handleAttach(ws, msg.sessionId, dims, Date.now())
+          session = manager.handleAttach(ws, msg.sessionId, dims, Date.now(), msg.cwd)
         } catch (err: unknown) {
           // M4: spawn failure — send exit(-1) and close only this connection.
           const reason =

src/session/manager.ts

@@ -82,11 +82,13 @@ export function createSessionManager(cfg: Config): SessionManager {
     sessionId: string | null,
     dims: Dims,
     now: number,
+    cwd?: string,
   ): Session {
     // ── Case 1: null → always create a new session ──────────────────────────
     if (sessionId === null) {
       // M4: createSession may throw (spawn failure). Do NOT catch here.
-      const session = createSession(cfg, dims, now, onSessionExit);
+      // M6: cwd (if given) is the spawn directory for "new tab here".
+      const session = createSession(cfg, dims, now, onSessionExit, undefined, cwd);
       const kicked = attachWs(session, ws);
       if (kicked !== null) kicked.close();
       sessions = new Map(sessions).set(session.meta.id, session);

src/session/session.ts

@@ -61,6 +61,8 @@ export function createSession(
   // H1: pass an existing id to RE-ATTACH to a surviving tmux session (e.g. after
   // a server restart). Default = a fresh id for a brand-new session.
   id: string = randomUUID(),
+  // M6: spawn directory for a new session ("new tab here"); defaults to homeDir.
+  cwd?: string,
 ): Session {
   // The id is injected into the shell env so Claude Code hooks know which tab an
   // event belongs to ($WEBTERM_SESSION) and where to POST ($WEBTERM_HOOK_URL, H2).
@@ -76,7 +78,7 @@ export function createSession(
     name: 'xterm-256color',
     cols: dims.cols,
     rows: dims.rows,
-    cwd: cfg.homeDir,
+    cwd: cwd ?? cfg.homeDir,
     env: {
       ...process.env,
       WEBTERM_SESSION: id,

src/types.ts

@@ -39,9 +39,10 @@ export type EnvLike = Readonly<Record<string, string | undefined>>;
 
 /* ─────────────────────── protocol (§3.2) ─────────────────────── */
 
-/** client → server. approve/reject (H3) resolve a held PermissionRequest. */
+/** client → server. approve/reject (H3) resolve a held PermissionRequest.
+ *  attach.cwd (M6) = spawn a new session in this directory ("new tab here"). */
 export type ClientMessage =
-  | { type: 'attach'; sessionId: string | null }
+  | { type: 'attach'; sessionId: string | null; cwd?: string }
   | { type: 'input'; data: string }
   | { type: 'resize'; cols: number; rows: number }
   | { type: 'approve' }
@@ -167,7 +168,13 @@ export interface Session {
 /* ──────────────────────── manager (§3.5) ─────────────────────── */
 
 export interface SessionManager {
-  handleAttach(ws: WebSocketLike, sessionId: string | null, dims: Dims, now: number): Session;
+  handleAttach(
+    ws: WebSocketLike,
+    sessionId: string | null,
+    dims: Dims,
+    now: number,
+    cwd?: string,
+  ): Session;
   get(id: string): Session | undefined;
   /** Set a session's Claude status (from a hook) and push it to the attached ws (H2/H3). */
   handleHookEvent(