Expose explicit LiveSync batching and honour save failures

Show the batching choice for the current synchronisation mode while
preserving both mode preferences. Observe local save failures before
file-open work and report failed asynchronous unload preparation.

Record the accepted recovery and batching contract, update the primary
settings documentation, and add two-device runtime coverage for batching,
deletions, saved settings, and interrupted local processing.

Requires Commonlib commit 72bdc66af5d7338d8f2f69ebe83c3866def93360.
Update the exact registry dependency when its package version is published.

Validation: full repository check; latest packed dependency type checks,
production build, 1,373 unit tests (one skipped), and six focused runtime
recovery cases. The earlier implementation passed the full 23-case runtime
comparison and five additional interruption conditions.

src/modules/features/SettingDialogue/PaneSyncSettings.ts

@@ -171,20 +171,18 @@ export function paneSyncSettings(
         }
     });
 
-    void addPanel(
-        paneEl,
-        $msg("obsidianLiveSyncSettingTab.titleUpdateThinning"),
-        undefined,
-        visibleOnly(() => !this.isConfiguredAs("syncMode", "LIVESYNC"))
-    ).then((paneEl) => {
-        new Setting(paneEl).autoWireToggle("batchSave");
+    void addPanel(paneEl, $msg("obsidianLiveSyncSettingTab.titleUpdateThinning")).then((paneEl) => {
+        const inLiveSyncMode = () => this.isConfiguredAs("syncMode", "LIVESYNC");
+        const batchEnabled = () => this.isConfiguredAs(inLiveSyncMode() ? "batchSaveInLiveSync" : "batchSave", true);
+        new Setting(paneEl).autoWireToggle("batchSave", { onUpdate: visibleOnly(() => !inLiveSyncMode()) });
+        new Setting(paneEl).autoWireToggle("batchSaveInLiveSync", { onUpdate: visibleOnly(inLiveSyncMode) });
         new Setting(paneEl).autoWireNumeric("batchSaveMinimumDelay", {
             acceptZero: true,
-            onUpdate: visibleOnly(() => this.isConfiguredAs("batchSave", true)),
+            onUpdate: visibleOnly(batchEnabled),
         });
         new Setting(paneEl).autoWireNumeric("batchSaveMaximumDelay", {
             acceptZero: true,
-            onUpdate: visibleOnly(() => this.isConfiguredAs("batchSave", true)),
+            onUpdate: visibleOnly(batchEnabled),
         });
     });