fix(directory-picker): address review — modal layering, root nav, stale state

- HIGH: the "Browse Folders..." entry in the New Session RN <Modal> expanded
  a sibling BottomSheet, which a native Modal always covers (a
  BottomSheetModal through the root portal would be covered too), so the
  primary entry point was invisible/untouchable. The modal is now closed
  before the sheet expands and restored on cancel via a new onDismiss
  callback (restoreNewSessionOnDismiss ref); picking a folder proceeds to
  session creation without reopening the modal.

- MEDIUM: parentOf("/") returned "/" so Up at the POSIX root looped forever;
  it now returns null at "/", "\" and Windows drive roots alike, disabling
  the Up button there.

- LOW: opening the sheet with no known start directory (server home not
  loaded yet) showed the previous open's stale entries; it now clears state,
  invalidates in-flight loads, and shows an "Enter a path above to start
  browsing" empty state. Sheet init also no longer re-runs on snap-point
  drags (wasOpen guard).

- Extracted the pure path helpers (stripTrailingSlash/parentOf/nameOf) into
  src/lib/path-utils.ts (no RN imports) with node --test coverage for POSIX
  root, Windows drive roots, trailing slashes, and backslash paths.

typecheck clean; 97/97 tests pass (16 new).

app/(tabs)/index.tsx

@@ -275,17 +275,28 @@ export default function SessionsScreen() {
     }
   }
 
+  // The browser sheet is a sibling of the New Session <Modal>. A native RN
+  // Modal layers above everything in the React root (including bottom-sheet
+  // portals), so the modal must be closed before the sheet is shown; this ref
+  // remembers to bring it back if the user cancels without picking a folder.
+  const restoreNewSessionOnDismiss = useRef(false)
+
   const openBrowser = useCallback(
     (startDir: string | null, mode: "create" | "switch") => {
       setBrowseStartDir(startDir || serverHome || null)
       setBrowseMode(mode)
+      if (mode === "create" && showNewSession) {
+        restoreNewSessionOnDismiss.current = true
+        setShowNewSession(false)
+      }
       browserSheetRef.current?.expand()
     },
-    [serverHome],
+    [serverHome, showNewSession],
   )
 
   const onBrowserSelect = useCallback(
     (directory: string) => {
+      restoreNewSessionOnDismiss.current = false
       if (browseMode === "switch") {
         handleSwitchDirectory(directory)
         dirSheetRef.current?.close()
@@ -296,6 +307,13 @@ export default function SessionsScreen() {
     [browseMode, handleSwitchDirectory, onCreateInDirectory],
   )
 
+  const onBrowserDismiss = useCallback(() => {
+    if (restoreNewSessionOnDismiss.current) {
+      restoreNewSessionOnDismiss.current = false
+      setShowNewSession(true)
+    }
+  }, [])
+
   const onFabPress = () => {
     // Quick create in current project
     onCreateSession()
@@ -666,6 +684,7 @@ export default function SessionsScreen() {
         clientForDirectory={clientForDirectory}
         isDark={isDark}
         onSelect={onBrowserSelect}
+        onDismiss={onBrowserDismiss}
       />
     </View>
   )