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/host/directory-picker-native/package.json

@@ -22,10 +22,6 @@
       "types": "./lib/types/invariant.d.ts",
       "default": "./lib/invariant.js"
     },
-    "./client": {
-      "types": "./lib/types/client/index.d.ts",
-      "default": "./lib/client.js"
-    },
     "./worker": {
       "types": "./lib/types/win32-dialog-worker.d.ts",
       "default": "./lib/worker.cjs"
@@ -37,7 +33,6 @@
     "lib/index.js",
     "lib/invariant.js",
     "lib/worker.cjs",
-    "lib/client.js",
     "lib/types/**/*.d.ts"
   ],
   "license": "BSD-3-Clause",
@@ -47,30 +42,12 @@
     "koffi": "^3.1.0"
   },
   "peerDependencies": {
-    "@deepseek-ai/dsh-client-runtime": "workspace:^",
-    "@deepseek-ai/dsh-client-ui-slots": "workspace:^",
-    "@deepseek-ai/dsh-client-ui-workspace": "workspace:^",
     "@deepseek-ai/dsh-invariants": "workspace:^",
-    "@deepseek-ai/cordis": "workspace:^",
-    "react": "^18.2.0"
+    "@deepseek-ai/cordis": "workspace:^"
   },
   "devDependencies": {
-    "@deepseek-ai/dsh-client-runtime": "workspace:^",
-    "@deepseek-ai/dsh-client-ui-slots": "workspace:^",
-    "@deepseek-ai/dsh-client-ui-workspace": "workspace:^",
     "@deepseek-ai/dsh-invariants": "workspace:^",
-    "@types/react": "~18.3.1",
     "@deepseek-ai/cordis": "workspace:^",
-    "react": "^18.2.0",
     "tsx": "^4.19.2"
-  },
-  "dsh": {
-    "client": {
-      "inject": [
-        "@deepseek-ai/dsh-client-runtime",
-        "@deepseek-ai/dsh-client-ui-workspace"
-      ],
-      "platform": "web"
-    }
   }
 }