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.

public/tabs.ts

@@ -151,7 +151,7 @@ export class TabApp {
 
   /* ── tab lifecycle ───────────────────────────────────────────── */
 
-  private addEntry(sessionId: string | null, customTitle: string | null): TabEntry {
+  private addEntry(sessionId: string | null, customTitle: string | null, cwd?: string): TabEntry {
     const entry: TabEntry = {
       session: null as unknown as TerminalSession,
       customTitle,
@@ -161,6 +161,7 @@ export class TabApp {
     }
     entry.session = new TerminalSession({
       sessionId,
+      ...(cwd !== undefined ? { cwd } : {}),
       onSessionId: () => this.persist(),
       // onActivity only fires for hidden (inactive) panes (see TerminalSession).
       onActivity: () => {
@@ -189,7 +190,9 @@ export class TabApp {
   }
 
   newTab(): void {
-    this.addEntry(null, null)
+    // M6: open the new tab in the active tab's current directory, if known.
+    const cwd = this.tabs[this.activeIndex]?.session.cwd ?? undefined
+    this.addEntry(null, null, cwd)
     this.persist()
     this.rebuild()
     this.activate(this.tabs.length - 1)

public/terminal-session.ts

@@ -14,7 +14,7 @@ import { FitAddon } from '@xterm/addon-fit'
 import { SearchAddon } from '@xterm/addon-search'
 import { WebLinksAddon } from '@xterm/addon-web-links'
 import type { ClaudeStatus, ClientMessage, ServerMessage } from '../src/types.js'
-import { folderFromTitle } from './title-util.js'
+import { folderFromTitle, cwdFromOsc7 } from './title-util.js'
 
 const RESET = '\x1b[0m'
 const BOLD = '\x1b[1m'
@@ -54,6 +54,8 @@ export interface TerminalSessionOpts {
   onStatus?: (status: SessionStatus) => void
   /** Optional: fired when Claude Code activity changes (from a hook, H2). */
   onClaudeStatus?: (status: ClaudeStatus, detail?: string) => void
+  /** Optional: spawn a NEW session in this directory ("new tab here", M6). */
+  cwd?: string
 }
 
 export class TerminalSession {
@@ -68,8 +70,10 @@ export class TerminalSession {
   private readonly onTitle: ((title: string) => void) | undefined
   private readonly onStatus: ((status: SessionStatus) => void) | undefined
   private readonly onClaudeStatus: ((status: ClaudeStatus, detail?: string) => void) | undefined
+  private readonly spawnCwd: string | undefined
   private statusValue: SessionStatus = 'connecting'
   private claudeStatusValue: ClaudeStatus = 'unknown'
+  private cwdValue: string | null = null
   private pendingApprovalValue = false
   private pendingToolValue: string | undefined = undefined
 
@@ -91,6 +95,7 @@ export class TerminalSession {
     this.onTitle = opts.onTitle
     this.onStatus = opts.onStatus
     this.onClaudeStatus = opts.onClaudeStatus
+    this.spawnCwd = opts.cwd
 
     this.el = document.createElement('div')
     this.el.className = 'term-pane'
@@ -111,6 +116,12 @@ export class TerminalSession {
     this.term.onData((data) => this.send(data))
     // Tab title = current folder, derived from the shell's OSC title.
     this.term.onTitleChange((title) => this.onTitle?.(folderFromTitle(title) ?? title))
+    // OSC 7 reports the full cwd (M6) — used for "new tab here".
+    this.term.parser.registerOscHandler(7, (payload) => {
+      const c = cwdFromOsc7(payload)
+      if (c !== null) this.cwdValue = c
+      return true
+    })
 
     this.resizeObserver = new ResizeObserver(() => this.scheduleResize())
     this.resizeObserver.observe(this.el)
@@ -131,6 +142,11 @@ export class TerminalSession {
     return this.claudeStatusValue
   }
 
+  /** Current working directory reported by the shell via OSC 7 (M6), or null. */
+  get cwd(): string | null {
+    return this.cwdValue
+  }
+
   /** Whether a tool approval is held server-side and can be resolved (H3). */
   get pendingApproval(): boolean {
     return this.pendingApprovalValue
@@ -189,7 +205,13 @@ export class TerminalSession {
       this.reconnectDelay = 1000
       this.setStatus('connected')
       this.term.write(statusLine(`${GREEN}${BOLD}Connected${RESET}`))
-      socket.send(buildMessage({ type: 'attach', sessionId: this.sessionId }))
+      // Send cwd only on a fresh session (M6 "new tab here"); on reconnect the
+      // sessionId is already set and the server ignores cwd.
+      const attachMsg: ClientMessage =
+        this.sessionId === null && this.spawnCwd !== undefined
+          ? { type: 'attach', sessionId: null, cwd: this.spawnCwd }
+          : { type: 'attach', sessionId: this.sessionId }
+      socket.send(buildMessage(attachMsg))
     })
 
     socket.addEventListener('message', (event: MessageEvent<string>) => {

public/title-util.ts

@@ -23,3 +23,19 @@ export function folderFromTitle(title: string): string | null {
   if (slash !== -1) s = s.slice(slash + 1)
   return s || null
 }
+
+/**
+ * Parse the full cwd path from an OSC 7 sequence payload (M6).
+ *   data = "file://host/Users/me/dir"  →  "/Users/me/dir"
+ * Returns null if it isn't a file:// URL.
+ */
+export function cwdFromOsc7(data: string): string | null {
+  const m = /^file:\/\/[^/]*(\/.*)$/.exec(data.trim())
+  if (m === null) return null
+  const path = m[1] as string
+  try {
+    return decodeURIComponent(path)
+  } catch {
+    return path
+  }
+}