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-browse/package.json

@@ -22,55 +22,25 @@
       "types": "./lib/types/invariant.d.ts",
       "default": "./lib/invariant.js"
     },
-    "./client": {
-      "types": "./lib/types/client/index.d.ts",
-      "default": "./lib/client.js"
-    },
     "./src/*": "./src/*",
     "./package.json": "./package.json"
   },
   "files": [
     "lib/index.js",
     "lib/invariant.js",
-    "lib/client.js",
     "lib/types/**/*.d.ts"
   ],
   "license": "BSD-3-Clause",
   "dependencies": {
     "@deepseek-ai/dsh-host-directory-picker": "workspace:^",
-    "clsx": "^2.0.0",
     "@deepseek-ai/schemastery": "workspace:^"
   },
   "peerDependencies": {
-    "@deepseek-ai/dsh-client-locale": "workspace:^",
-    "@deepseek-ai/dsh-client-runtime": "workspace:^",
-    "@deepseek-ai/dsh-client-ui-primitives": "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-locale": "workspace:^",
-    "@deepseek-ai/dsh-client-runtime": "workspace:^",
-    "@deepseek-ai/dsh-client-test-runtime": "workspace:^",
-    "@deepseek-ai/dsh-client-ui-primitives": "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"
-  },
-  "dsh": {
-    "client": {
-      "inject": [
-        "@deepseek-ai/dsh-client-runtime",
-        "@deepseek-ai/dsh-client-ui-workspace",
-        "@deepseek-ai/dsh-client-locale"
-      ],
-      "platform": "web"
-    }
+    "@deepseek-ai/cordis": "workspace:^"
   }
 }