feat: LinkedIn LLM alignment - Phase 1-3 complete

Phase 1: Dead Code Cleanup
- Remove GeminiGroundedProvider import and property from linkedin_service.py
- Remove fallback_provider property (gemini_provider imports)
- Fix routers/linkedin.py edit endpoint to use llm_text_gen
- Delete dead LinkedInImageEditor class
- Remove dead _transform_gemini_sources from content_generator.py

Phase 2: Research Infrastructure Alignment
- Add user_id to _conduct_research() for pre-flight validation
- Add validate_exa_research_operations() before Exa/Tavily calls
- Pass user_id to provider.simple_search() for usage tracking
- Inject research content into LLM prompts via _build_research_context()
- Fix Google engine path to fallback to Exa
- Add Exa → Tavily fallback on research failure

Phase 3: Cosmetic Cleanup
- Rename _generate_prompts_with_gemini → _generate_prompts_with_llm
- Rename _build_gemini_prompt → _build_image_prompt
- Rename _parse_gemini_response → _parse_llm_response
- Remove all Gemini references from LinkedIn code (0 remaining)
- Update docstrings and log messages

Additional:
- Research caching using existing ResearchCache
- Shared ExaContentResearchProvider in services/research/
- Persona service uses llm_text_gen instead of gemini_structured_json_response
- LinkedInWriter.tsx ChatMessage → ChatMsg type mapping fix
- RegisterLinkedInActionsEnhanced.tsx content_format_rules typing fix

backend/services/linkedin/content_generator_prompts/carousel_generator.py

@@ -96,7 +96,7 @@ class CarouselGenerator:
                 'data': carousel_content,
                 'research_sources': research_sources,
                 'generation_metadata': {
-                    'model_used': 'gemini-2.0-flash-001',
+                    'model_used': 'llm_text_gen',
                     'generation_time': generation_time,
                     'research_time': research_time,
                     'grounding_enabled': grounding_enabled

backend/services/linkedin/content_generator_prompts/video_script_generator.py

@@ -81,7 +81,7 @@ class VideoScriptGenerator:
                 'data': video_script,
                 'research_sources': research_sources,
                 'generation_metadata': {
-                    'model_used': 'gemini-2.0-flash-001',
+                    'model_used': 'llm_text_gen',
                     'generation_time': generation_time,
                     'research_time': research_time,
                     'grounding_enabled': grounding_enabled