Context

PR 4/N in the test-suite-green effort. Fixes the 7 tests in
tests/tools/test_browser_chromium_check.py, which all share one root cause in
the Chromium-presence detection used by the browser tool's fast-fail guard.

Tests fixed (7)

• TestChromiumInstalled::test_false_when_dir_empty
• TestChromiumInstalled::test_false_when_only_unrelated_browsers
• TestChromiumInstalled::test_false_when_path_not_a_dir
• TestCheckBrowserRequirementsChromium::test_local_mode_missing_chromium_returns_false
• TestRunBrowserCommandChromiumGuard::test_local_mode_missing_chromium_returns_error_immediately
• TestRunBrowserCommandChromiumGuard::test_docker_hint_mentions_image_pull
• TestRunBrowserCommandChromiumGuard::test_non_docker_hint_mentions_agent_browser_install

Root cause

_chromium_installed() probed shutil.which("google-chrome" / "chromium-browser" / "chrome") before scanning the Playwright browser cache. On any machine
with a system Chrome on PATH (CI runners, dev boxes), that short-circuited to
True even when no Playwright / agent-browser build existed.

The tests deliberately scope detection to an empty PLAYWRIGHT_BROWSERS_PATH
and patch os.path.expanduser, expecting False — but they don't (and
shouldn't have to) neutralize a stray system Chrome on PATH. So the
fast-fail guard in _run_browser_command never fired, subprocess.Popen was
reached, and the "Should have failed before spawning subprocess" assertion
tripped (plus the is False assertions).

Sample failure on a runner with Chrome present:
AssertionError: assert 'Chromium' in 'Should have failed before spawning subprocess'.

This is environment-fragile behavior: green on a machine without Chrome,
red on one with it — matching the "pre-existing failures on main" pattern.

Fix

Removed the unconditional system-Chrome-on-PATH probe. Playwright-driven
agent-browser does not auto-adopt an arbitrary system Chrome unless explicitly
pointed there via AGENT_BROWSER_EXECUTABLE_PATH (check #1, retained), so the
bare PATH probe was both a false positive and not how the browser is actually
resolved at runtime. The explicit env override and the Playwright cache scan
remain authoritative. One commit, one file (tools/browser_tool.py,
+14/-14, mostly the renumbered docstring).

Validation

# WITH google-chrome on PATH (reproduces the CI failure condition)
$ PATH="/tmp/fakebin:$PATH" pytest tests/tools/test_browser_chromium_check.py -n0
  before: 7 failed, 9 passed
  after:  16 passed

# clean environment
$ pytest tests/tools/test_browser_chromium_check.py -n0
  16 passed

# related suites (no regressions)
$ pytest test_browser_chromium_check test_browser_lightpanda \
         test_browser_homebrew_paths test_browser_orphan_reaper -n0
  98 passed

Remaining on main

~38 pre-existing failures reported on main at the start of this effort; this
PR removes 7 of them. (Two unrelated MCP test files —
test_mcp_oauth_metadata.py, test_mcp_tool.py — have import-time collection
errors that are out of scope here.)