refactor(picker): split the directory-picker faces into their own packages

The browse and native backends were dual-face packages: a Node backend plus a
browser surface under one tsconfig that referenced Client packages. That put
Client projects — and through them the Client runtime — inside the Host
compiler aggregate, which builds before the generated Remote contributions
exist. Each browser half moves to its own Client package, and both backends
become Node-only.

The interaction is still one choice: the adaptive chooser mounts the backend
and its surface as a pair of Loader entries and tears both down in reverse, so
a resolved kind still swaps both faces. Compositions that pin an interaction
directly now pin the pair, and the chooser's runtime-string package list keeps
naming everything a composing app must resolve.

apps/cli/tests/web-agent-presets.e2e.ts

@@ -86,7 +86,10 @@ async function bootWeb(settingsFile: string, extra: PatchOptions[] = []): Promis
     // host and so waits for the webserver disabled above; the browse variant
     // supplies `directoryPicker` without one.
     { id: 'directory-picker', disabled: true },
-    { insert: [{ id: 'directory-picker-browse', name: '@deepseek-ai/dsh-host-directory-picker-browse' }] },
+    { insert: [
+      { id: 'directory-picker-browse', name: '@deepseek-ai/dsh-host-directory-picker-browse' },
+      { id: 'ui-directory-picker', name: '@deepseek-ai/dsh-client-ui-directory-picker' },
+    ] },
     // The roster AppCLIEntry would patch in; only the shipped root, so a
     // developer's own `~/.dsh/.preset` cannot change this test's outcome.
     // `default` here is the COMPOSITION default — the base layer the settings

apps/web/tests/pin-browse-picker.overlay.yml

@@ -9,3 +9,5 @@
 - insert:
     - id: directory-picker-browse
       name: '@deepseek-ai/dsh-host-directory-picker-browse'
+    - id: ui-directory-picker
+      name: '@deepseek-ai/dsh-client-ui-directory-picker'

apps/web/tests/scaffold.ts

@@ -439,7 +439,10 @@ export async function launchWebScaffold(options: LaunchOptions = {}): Promise<We
     // host: patch `name` is an assertion, not an override, hence the
     // disable+insert pair.
     { id: 'directory-picker', disabled: true },
-    { insert: [{ id: 'directory-picker-browse', name: '@deepseek-ai/dsh-host-directory-picker-browse' }] },
+    { insert: [
+      { id: 'directory-picker-browse', name: '@deepseek-ai/dsh-host-directory-picker-browse' },
+      { id: 'ui-directory-picker', name: '@deepseek-ai/dsh-client-ui-directory-picker' },
+    ] },
     ...options.agentPresets === undefined
       ? []
       : [{ id: 'agent-presets', config: options.agentPresets }],