Add PostgresSubprocessException and refactor database initialization logic

- Introduced PostgresSubprocessException to handle errors during PostgreSQL subprocess execution.
- Refactored PostgresDatabaseProvider to improve schema initialization script discovery.
- Enhanced error handling for psql command execution, including logging of output and errors.
- Implemented methods to find the schema initialization script and the psql executable path.

docs/SCHEMA_CONVERSION_GUIDE.md

@@ -156,7 +156,7 @@ Update system table for consistency:
 ---
 
 ## File Location
-- **Source**: `Jellyfin.Server/sql/schema_init/create_database_schema.sql` (1879 lines)
+- **Source**: `scripts/sql/schema_init/create_database_schema.sql` (1879 lines)
 - **Output**: Same file (in-place conversion)
 
 ---