tests/test_playwrightprovider: assert browsers live under install_root/cache

Devin caught the test drift from the PLAYWRIGHT_BROWSERS_PATH rework:
browsers now land in ``<install_root>/cache/chromium-<buildId>/``
(matching the ``install_root/cache`` default abxpkg pins), not
directly under ``install_root``. Update every place that iterates
``playwright_root`` or ``install_root`` looking for ``chromium-*/``
dirs to walk ``<root>/cache`` instead — covering the chromium install
lifecycle assertions, the ``--no-shell`` carveout check, the update
test's resolved-target ancestry check, and the dry-run "no browsers
got downloaded" check.

Also points the symlink ancestry assertion in
``test_chromium_install_puts_real_browser_into_managed_bin_dir`` at
``playwright_root/cache`` since that's the actual
``PLAYWRIGHT_BROWSERS_PATH`` root the symlinks resolve into.

Author: claude

tests/test_playwrightprovider.py

@@ -70,14 +70,14 @@ def test_chromium_install_puts_real_browser_into_managed_bin_dir(
             assert provider.bin_dir is not None
             assert installed.loaded_abspath.parent == provider.bin_dir
             assert installed.loaded_abspath == provider.bin_dir / "chromium"
-            # The symlink resolves into playwright_root (which is also
-            # PLAYWRIGHT_BROWSERS_PATH for this provider).
+            # The symlink resolves into ``playwright_root/cache`` (the
+            # managed ``PLAYWRIGHT_BROWSERS_PATH`` for this provider).
             real_target = installed.loaded_abspath.resolve()
-            assert playwright_root.resolve() in real_target.parents
+            assert (playwright_root / "cache").resolve() in real_target.parents
             # Playwright lays out chromium builds as chromium-<build>/.
             assert any(
                 child.name.startswith("chromium-")
-                for child in playwright_root.iterdir()
+                for child in (playwright_root / "cache").iterdir()
                 if child.is_dir()
             )
 
@@ -134,7 +134,7 @@ def test_install_root_alias_without_explicit_bin_dir_uses_root_bin(
             # the effective PLAYWRIGHT_BROWSERS_PATH for this provider).
             assert any(
                 child.name.startswith("chromium-")
-                for child in install_root.iterdir()
+                for child in (install_root / "cache").iterdir()
                 if child.is_dir()
             )
 
@@ -171,7 +171,7 @@ def test_install_root_and_bin_dir_aliases_install_into_the_requested_paths(
             # Browser tree still landed in install_root, not bin_dir.
             assert any(
                 child.name.startswith("chromium-")
-                for child in install_root.iterdir()
+                for child in (install_root / "cache").iterdir()
                 if child.is_dir()
             )
 
@@ -244,9 +244,10 @@ def test_provider_install_args_are_passed_through_to_playwright_install(
             assert installed is not None
             assert installed.loaded_abspath is not None
             assert installed.loaded_abspath.exists()
+            cache_dir = playwright_root / "cache"
             chromium_dirs = [
                 child
-                for child in playwright_root.iterdir()
+                for child in cache_dir.iterdir()
                 if child.is_dir()
                 and child.name.startswith("chromium-")
                 and not child.name.startswith("chromium_headless_shell")
@@ -255,7 +256,7 @@ def test_provider_install_args_are_passed_through_to_playwright_install(
             # ``--no-shell`` should have skipped the headless shell download.
             headless_shell_dirs = [
                 child
-                for child in playwright_root.iterdir()
+                for child in cache_dir.iterdir()
                 if child.is_dir() and child.name.startswith("chromium_headless_shell")
             ]
             assert not headless_shell_dirs, (
@@ -380,10 +381,10 @@ def test_update_refreshes_chromium_in_place(
             # ``playwright_root``).
             updated_target = updated.loaded_abspath.resolve()
             assert updated_target.exists()
-            assert playwright_root.resolve() in updated_target.parents
+            assert (playwright_root / "cache").resolve() in updated_target.parents
             assert any(
                 child.name.startswith("chromium-")
-                for child in playwright_root.iterdir()
+                for child in (playwright_root / "cache").iterdir()
                 if child.is_dir()
             )
 
@@ -397,14 +398,15 @@ def test_provider_dry_run_does_not_install_chromium(self, test_machine):
 
             test_machine.exercise_provider_dry_run(provider, bin_name="chromium")
             # dry_run must not have actually downloaded any browsers.
+            cache_dir = playwright_root / "cache"
             browser_dirs = (
                 [
                     p
-                    for p in playwright_root.iterdir()
+                    for p in cache_dir.iterdir()
                     if p.is_dir()
                     and p.name.startswith(("chromium-", "firefox-", "webkit-"))
                 ]
-                if playwright_root.is_dir()
+                if cache_dir.is_dir()
                 else []
             )
             assert not browser_dirs, (