feat(docker): add a folder picker to both path fields

Both paths in the adoption form had to be typed. Each gets a Browse button
using the same path-input-group markup Link Existing uses, so the two look and
behave alike.

What they can browse differs, and that is the point. The host workspace path
reuses the existing host picker. The container workdir cannot: an adopted
container has nothing mounted at a matching host path, so a host listing would
be a different filesystem — and getting this field wrong is the source of the
opaque OCI chdir error at launch, which makes it the field that most needs to
be clickable.

Adds a read-only POST /api/docker-cases/browse: one `ls` through docker exec, no
writes, no lifecycle, path shell-escaped like every other value. `ls -Ap` marks
directories with a trailing slash and keeps names with spaces intact.

PathPicker takes an optional fetchListing source rather than being forked: the
container variant only swaps where the rows come from, and reuses the rendering,
navigation, Up and Choose/Select unchanged.

src/web/schemas.ts

@@ -867,6 +867,22 @@ export const DockerAdoptPreflightSchema = z.object({
     .optional(),
 });
 
+/** Read-only directory listing inside a container (adoption workdir picker). */
+export const DockerBrowseSchema = z.object({
+  hostId: z.string().regex(/^[a-zA-Z0-9_-]+$/, 'Invalid docker host id'),
+  container: z
+    .string()
+    .min(2)
+    .max(128)
+    .regex(/^[a-zA-Z0-9][a-zA-Z0-9_.-]+$/, 'Invalid container name'),
+  path: z
+    .string()
+    .max(2000)
+    .regex(/^\//, 'Path must be absolute')
+    .regex(NO_SHELL_META, 'Invalid characters in path')
+    .optional(),
+});
+
 export const DockerExportSchema = z.object({
   mode: z.enum(['full', 'workspace']).optional(),
 });