Make Copy to… and Cut to… the selection bar's actions

The selection bar offered Copy and Move, which only filled an in-app clipboard; the
destination picker then lived behind an overflow menu, and Paste in the top bar. That
made a copy a two-step detour through another folder - the thing M16's picker exists to
avoid.

- The bar's two verbs are now Copy to… and Cut to…, both opening the destination picker.
- The clipboard state, Paste here, and the overflow's duplicate Copy to… / Move to… are
  removed. The picker's cut title and confirm are Cut to… / Cut here.
- A copy still keeps the selection for a second destination; a cut clears it. Conflicts
  still ask before overwriting, naming the picked folder.
- Five clipboard tests are removed; the mark, restart and undo tests now use the picker.
  BrowserTopBar's search and overflow sections are extracted so its two new detekt
  findings are fixed rather than baselined.

Driven on the Xiaomi phone: Copy to… copied 120 x 16 MB through Internal storage ->
AADemo -> Target and reported Copied 121 items to Target; Cut to… moved file001.bin and
offered Undo; a name in the way raised Items already exist here; the top-bar overflow
has no Paste. The foreground-service video was re-recorded against the new bar at 16.1 s.

Verified: ./tools/verify.sh green, the code map current, 426 unit tests pass, and the
video decodes as H.264 1080x2400 with no audio.

docs/PLAY_RELEASE_CHECKLIST.md

@@ -183,8 +183,8 @@ asks about this separately from All files access.
 
 - **Use case: Local processing → Importing, exporting.** Play's own chart describes the use case as
   *"Includes migration of files from SD card. Show the user manually triggering an import or export
-  of files locally (for example, as moving files from an SD card)"* — which is what **Paste** and
-  **Copy to… / Move to…** do. Do **not** tick network processing, backing up/restoring, media
+  of files locally (for example, as moving files from an SD card)"* — which is what **Copy to…** and
+  **Cut to…** do. Do **not** tick network processing, backing up/restoring, media
   transcoding or "Other tasks": every `OperationKind` is local — `COPY`, `MOVE`, `DELETE`, `COMPRESS`,
   `EXTRACT` — and none of them touches a network.
 
@@ -204,10 +204,11 @@ asks about this separately from All files access.
   the destination, and the user has to start the operation again. Nothing is overwritten without
   asking, and deletes are staged in the 24-hour trash, so completed deletes remain recoverable."*
 
-- [ ] **Upload the foreground-service video.** `store-assets/video/fgs-import-export.mp4` (**18.0 s**,
+- [ ] **Upload the foreground-service video.** `store-assets/video/fgs-import-export.mp4` (**16.1 s**,
       captions burned in) to YouTube **Unlisted** or Drive with link sharing, then paste that URL into
-      the foreground-service declaration. It shows the selection, **Copy**, **Paste here**, the
-      **Copying files** notification with its progress bar, and the completed folder. It is a
+      the foreground-service declaration. It shows the selection, **Copy to…**, the destination
+      picker (`Internal storage → AADemo → Target`), **Copy here**, the **Copying files**
+      notification with its progress bar, and **Copied 121 items to Target**. It is a
       different field from the All files access video. What was cut, the privacy checks, and how to
       re-shoot it: [FGS_VIDEO](FGS_VIDEO.md).