feat(v0.6): Project Manager — repo discovery + Projects panel + tab wiring

Home screen gains a Sessions↔Projects segmented control. The Projects view
discovers the host's git repos and, on click, opens a tab named after the
repo, spawned in the repo dir, auto-running `claude` (1:N sessions per project).

Backend (P2/P4):
- src/http/projects.ts — parseGitHead + buildProjects(cfg, liveSessions):
  depth-capped BFS for .git (skips node_modules/dotdirs/symlinks, stops
  descending at a repo), .git/HEAD branch parse, rate-limited `git status`
  dirty check (execFile, no shell, 2s timeout, concurrency 8), merge of
  ~/.claude/projects cwds (reuses history.listSessions), cwd-prefix session
  merge (fresh each call), TTL discovery cache with in-flight dedup.
- src/server.ts — read-only GET /projects (no Origin guard, []-fallback).

Frontend (P5/P6):
- public/projects.ts — mountProjects: 1:N cards (branch chip, dirty dot,
  session rows, "+ start claude here"), live search, localStorage favourites;
  pure helpers extracted for unit tests.
- public/tabs.ts — openProject (#n suffix for dup names, sends 'claude\r'),
  countOpenWithTitlePrefix, Sessions↔Projects home toggle (updateHomeView).
- public/style.css — Projects panel + .home-seg control styles.

Config (P3, hardened): PROJECT_ROOTS/SCAN_DEPTH/SCAN_TTL/DIRTY_CHECK already
added; this commit adds fail-fast rejection of relative PROJECT_ROOTS.

Review hardening (4 confirmed HIGH + boundary validation):
- carriage-return fix so claude auto-executes (A3); seg-control z-order;
  parallelised history merge; concurrent-cache-miss dedup.
- normalizeProject guards the /projects response; getFavs filters non-strings.

Tests: +57 (398 total). Backend src/http/projects.ts 93.4%, config.ts 98%.
Verified: both typechecks clean, full suite green, build:web OK, coverage
≥80×4, real-browser smoke (83 repos, branch/dirty correct, click→claude tab).

src/config.ts

@@ -7,6 +7,7 @@
  */
 
 import os from 'node:os'
+import path from 'node:path'
 import type { Config, EnvLike } from './types.js'
 import { tmuxAvailable } from './session/tmux.js'
 
@@ -70,6 +71,16 @@ function parseProjectRoots(raw: string | undefined, homeDir: string): readonly s
     .map((s) => s.trim())
     .filter((s) => s !== '')
     .map((s) => (s === '~' ? homeDir : s.startsWith('~/') ? homeDir + s.slice(1) : s))
+  // Fail fast on relative roots: silently resolving them against the server's
+  // CWD makes the scan target depend on where the process was launched (M1-style
+  // "no surprising defaults"). Require absolute paths (after '~' expansion).
+  for (const r of roots) {
+    if (!path.isAbsolute(r)) {
+      throw new Error(
+        `Invalid config: PROJECT_ROOTS entry ${JSON.stringify(r)} — must be an absolute path (or '~' / '~/...').`,
+      )
+    }
+  }
   return Object.freeze(roots.length > 0 ? roots : [homeDir])
 }