feat(host,client): ship the in-app directory browser as the browse package's client half

directory-picker-browse becomes dual-face: its browser half fills
ui-workspace's two directory-flow holes with the Select Workspace Directory
dialog (figma Harness 813-23126 family — Miller two-column view, breadcrumb
with click-to-edit path zone, nested New-folder dialog), driving the node
half's host.listDirectory/host.createDirectory and owning its locale
namespace (directory-browser, zh default / en). The dialog moves here from
ui-workspace wholesale — the trigger surfaces keep only the flow-hole owner
conversation.

apps/cli flips its one directory-picker row -native -> -browse, swapping the
host backend and the client interaction together; picking now works for
remote deployments out of the box. The keyless workspace-flow snapshot boots
the browse bundle and drives menu -> dialog -> Documents -> project -> Open
against the fixture tree.

tsconfig.client.json

@@ -19,6 +19,8 @@
     "packages/client/*/src/css-modules.d.ts",
     "packages/client/*/tests/**/*.ts",
     "packages/client/*/tests/**/*.tsx",
+    "packages/host/directory-picker-browse/tests/**/*.ts",
+    "packages/host/directory-picker-browse/tests/**/*.tsx",
     "packages/host/directory-picker-native/tests/**/*.ts",
     "packages/host/directory-picker-native/tests/**/*.tsx",
     "packages/client/tsdown.client.ts",
@@ -33,6 +35,7 @@
     // browser half registers the picking flow into ui-workspace's slot —
     // client-side Context merges keep it out of the host program.
     { "path": "./packages/host/directory-picker-native" },
+    { "path": "./packages/host/directory-picker-browse" },
     { "path": "./packages/client/ui-slots" },
     { "path": "./packages/client/ui-primitives" },
     { "path": "./packages/client/web-react" },