test: integration-test the mode persist-on-unload wiring (#14)

The post-/runda DA pass on 4cd574b found the persist-on-unload wiring
(quit + project switch calling Database::set_mode) had no integration
test — only the db-level set_mode behaviour was covered, not that the
runtime actually invokes it on unload.

Add runtime::switch_persists_the_outgoing_projects_mode, driving the
real handle_project_switch end-to-end and asserting the outgoing
project's project.yaml recorded the mode it was left in. Red-first
verified: with the set_mode call disabled it fails (None vs
Some(Advanced)). The quit unload site shares the same set_mode call;
Action::Quit emission is already covered in app tests.

Updates ADR-0015 Amendment 1 coverage note.

docs/adr/0015-project-storage-runtime.md

@@ -677,9 +677,13 @@ time").
   (the teacher-export round-trip); `cli` `--mode` parse/precedence;
   `app::{mode_command_changes_mode_and_emits_persist_action,
   mode_command_via_one_shot_escape_persists_advanced,
-  project_switched_event_restores_the_stored_mode}`. The runtime's
-  unload call sites (quit + `handle_project_switch`) are thin
-  wiring over the tested `Database::set_mode`.
+  project_switched_event_restores_the_stored_mode}`;
+  `runtime::switch_persists_the_outgoing_projects_mode` — an
+  integration test driving the real `handle_project_switch` to
+  prove the unload wiring calls `set_mode` (red-first verified).
+  The quit unload site shares that `set_mode` call; the
+  `Action::Quit` emission is covered by `app`'s
+  `quit_command_returns_quit_action` / `ctrl_c_returns_quit_action`.
 
 ### Relationship to the Iteration 6 backlog