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/tsdown.config.ts

@@ -1,3 +1,15 @@
-import { clientBundle } from '../../client/tsdown.client.ts'
+import { defineConfig } from 'tsdown'
 
-export default clientBundle('@deepseek-ai/dsh-host-directory-picker-browse', ['lib/types/index.js', 'lib/types/invariant.js'])
+/** Node-only backend: listing and creation primitives over the host filesystem. */
+export default defineConfig([
+  {
+    entry: ['lib/types/index.js', 'lib/types/invariant.js'],
+    outDir: 'lib',
+    format: ['esm'],
+    platform: 'node',
+    target: 'es2024',
+    fixedExtension: false,
+    dts: false,
+    clean: false,
+  },
+])