refactor: simplify database logging handler

- Remove retry logic from DatabaseLogHandler (was for SQLite locking)
- Streamline error handling in log emission
- Clean up platform health service

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

app/core/lifespan.py

@@ -47,9 +47,12 @@ def check_database_ready():
     """Check if database is ready (migrations have been run)."""
     try:
         with engine.connect() as conn:
-            # Try to query a table that should exist
+            # Check for tables in the public schema (PostgreSQL)
             result = conn.execute(
-                text("SELECT name FROM sqlite_master WHERE type='table' LIMIT 1")
+                text(
+                    "SELECT tablename FROM pg_catalog.pg_tables "
+                    "WHERE schemaname = 'public' LIMIT 1"
+                )
             )
             tables = result.fetchall()
             return len(tables) > 0