fix(docsync): stop a push from stealing another file's pairing

Papra answers a push of bytes it already holds with the document that has
them. Two trip files with the same content therefore pushed to one document,
and the unique index on (link_id, remote_id) aborted that run and every run
after it with a constraint error. The pairing now stays with the file that
owns it and the second file is recorded as a conflict.

Also in this pass:
- Paperless no longer adopts a same-bytes document that lacks the scope's tag
  when a consume outlives the poll budget; that document belongs to someone
  else's filing and delete-through would have trashed it.
- The pull path writes the file row, the retirement of the copy it replaces
  and the pairing in one transaction, and announces them only once committed.
- PATCH links stops accepting remoteRootId/remoteRootPath, which it read and
  silently dropped.
- The MCP sync tool clears shelved items before running, as the REST route
  does.

server/src/nest/doc-sync/doc-sync-webhook.controller.ts

@@ -100,14 +100,20 @@ export class DocSyncWebhookController implements OnModuleDestroy {
    * up again when the timer fires, so a binding switched off or deleted in the
    * meantime does not get one last run out of a stale row.
    */
-  private schedule(linkId: number, reload: () => ReturnType<DocSyncConfigService['getLink']>): void {
+  private schedule(linkId: number, reload: () => ReturnType<DocSyncConfigService['getLink']>, isRetry = false): void {
     if (this.pending.has(linkId)) return;
     const timer = setTimeout(() => {
       this.pending.delete(linkId);
       const fresh = reload();
       if (!fresh || fresh.sync_enabled !== 1) return;
       if (!this.syncIsOn()) return;
-      void this.sync.syncLink(fresh);
+      void this.sync.syncLink(fresh).then((res) => {
+        // A run that was already in flight answers `busy`, and the changes this
+        // nudge was about may have landed after that run read the folder. Ask
+        // again once rather than waiting out a whole poll interval — once, and
+        // only for `busy`, so this cannot become a loop.
+        if (res?.state === 'busy' && !isRetry) this.schedule(linkId, reload, true);
+      });
     }, WEBHOOK_NUDGE_DEBOUNCE_SECONDS * 1000);
     // A pending nudge must not hold the process open at shutdown.
     if (typeof timer.unref === 'function') timer.unref();