feat(linkedin): integrate state-updater.mjs across all commands and hooks

Replace manual YAML editing instructions with deterministic
state-updater.mjs calls in 8 content commands (post, quick, react,
pipeline, first-post, video, publish, carousel) and 2 hook prompts
(state-update-reminder, post-creation-automation). Batch.md gets note
that state updates happen at publish time.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

plugins/linkedin-thought-leadership/commands/carousel.md

@@ -192,6 +192,17 @@ Offer refinement options as text (no interactive prompt):
 
 ## Step 7: State Update
 
-If the user confirms the carousel is ready:
-- Note in state file: topic, format=carousel, slide count
-- Suggest: "After publishing, run the 5x5x5 engagement method for maximum reach."
+If the user confirms the carousel is ready, update state deterministically:
+```bash
+node --input-type=module -e "
+import { writeState, updatePostTracking } from '${CLAUDE_PLUGIN_ROOT}/hooks/scripts/state-updater.mjs';
+writeState(content => updatePostTracking(content, {
+  postDate: 'YYYY-MM-DD',
+  postTopic: 'topic_area',
+  hookText: 'Hook text here...',
+  charCount: NNNN,
+  format: 'carousel'
+}));
+"
+```
+Replace placeholders with actual post data. Suggest: "After publishing, run the 5x5x5 engagement method for maximum reach."