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/__init__.py

@@ -17,13 +17,13 @@ from .content_generator_prompts import (
     VideoScriptGenerator
 )
 
-# Import new image generation services
+# Import image generation services
 from .image_generation import (
     LinkedInImageGenerator,
-    LinkedInImageEditor,
     LinkedInImageStorage
 )
 from .image_prompts import LinkedInPromptGenerator
+from .carousel import LinkedInCarouselPDFRenderer
 
 __all__ = [
     # Content Generation
@@ -42,9 +42,10 @@ __all__ = [
     
     # Image Generation Services
     'LinkedInImageGenerator',
-    'LinkedInImageEditor',
     'LinkedInImageStorage',
-    'LinkedInPromptGenerator'
+    'LinkedInPromptGenerator',
+    # Carousel Rendering
+    'LinkedInCarouselPDFRenderer',
 ]
 
 # Version information