feat: subfolder support in file sharing + directory browser UI

- FolderPicker: uses webkitRelativePath so paths like docs/report.pdf
  are preserved; adds "include subfolders" checkbox (default on)
- FileBrowser: virtual directory tree with breadcrumb navigation,
  sort by name/size, search filter, folders shown before files
- Protocol: browse sends path alongside name; get uses path as key
- FileEntry type gains optional path field

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

web/src/types.ts

@@ -29,6 +29,7 @@ export interface ChatMessage {
 export interface FileEntry {
   name: string
   size_bytes: number
+  path?: string  // relative path including filename, e.g. "docs/report.pdf"
 }
 
 export interface FileOffer {