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/DATABASE_MISMATCH_VISUAL_COMPARISON.md

@@ -308,7 +308,7 @@ STACK TRACE:
 AFFECTED FILES:
 
 SQL Schema:
-  └─ Jellyfin.Server/sql/schema_init/create_database_schema.sql
+  └─ scripts/sql/schema_init/create_database_schema.sql
 	 Lines: 92-886 (31 tables with PascalCase names)
 
 C# Configuration:

docs/DATABASE_SCHEMA_MISMATCH_REPORT.md

@@ -453,7 +453,7 @@ public void ConfigureConventions(ModelConfigurationBuilder configurationBuilder)
    - `src/Jellyfin.Database/Jellyfin.Database.Implementations/ModelConfiguration/`
 
 ### Database Schema Files
-1. `Jellyfin.Server/sql/schema_init/create_database_schema.sql`
+1. `scripts/sql/schema_init/create_database_schema.sql`
    - Lines 92-886 (all table definitions)
 
 ---

docs/QUICK_PUBLISH_REFERENCE.md

@@ -81,7 +81,7 @@ Creates 23 performance indexes automatically
 
 1. **`publish-with-sql.ps1`** - Automated publish + copy script ⭐
 2. **`copy-sql-files.ps1`** - Manual copy script
-3. **`Jellyfin.Server/sql/`** - SQL files directory
+3. **`scripts/sql/`** - SQL files directory
 
 ---
 

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)
 
 ---

docs/SQL_PUBLISH_ISSUE_RESOLVED.md

@@ -42,7 +42,7 @@ dotnet publish Jellyfin.Server\Jellyfin.Server.csproj -c Release
 ### Solution 3: Fixed Project Structure
 
 **Changed:**
-- Copied SQL files from `sql/` to `Jellyfin.Server/sql/`
+- Copied SQL files from `sql/` to `scripts/sql/`
 - Updated `Jellyfin.Server.csproj` to include them
 - Files are now part of the project directly
 
@@ -198,7 +198,7 @@ psql -U jellyfin -d jellyfin -c "SELECT COUNT(*) FROM pg_indexes WHERE indexname
 
 **Problem**: SQL files not included in publish  
 **Cause**: Files were outside project directory  
-**Fix**: Moved SQL files to `Jellyfin.Server/sql/` and created automated scripts  
+**Fix**: Moved SQL files to `scripts/sql/` and created automated scripts  
 **Result**: SQL files now automatically included in publish  
 
 ### What You Get: