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.

packages/bundle/web-app/package.json

@@ -56,6 +56,8 @@
     "@deepseek-ai/dsh-client-ui-command": "workspace:^",
     "@deepseek-ai/dsh-client-ui-conversation": "workspace:^",
     "@deepseek-ai/dsh-client-ui-deliverables": "workspace:^",
+    "@deepseek-ai/dsh-client-ui-directory-picker": "workspace:^",
+    "@deepseek-ai/dsh-client-ui-directory-picker-native": "workspace:^",
     "@deepseek-ai/dsh-client-ui-goal": "workspace:^",
     "@deepseek-ai/dsh-client-ui-layout": "workspace:^",
     "@deepseek-ai/dsh-client-ui-model": "workspace:^",