Add automatic PostgreSQL database creation and migration

- Added Jellyfin.Database.Providers.Postgres project with full EF Core migration support for PostgreSQL.
- Implemented automatic database creation and privilege assignment on startup.
- Generated initial migration and model snapshot for PostgreSQL schema.
- Updated build, test, and dependency files to include PostgreSQL provider and Npgsql packages.
- Added PowerShell script for generating and testing PostgreSQL migrations.
- No changes to application logic outside database provider/migration infrastructure.

tests/Jellyfin.Server.Implementations.Tests/obj/Jellyfin.Server.Implementations.Tests.csproj.nuget.dgspec.json

@@ -2543,6 +2543,9 @@
               "E:\\Projects\\pgsql-jellyfin\\src\\Jellyfin.Database\\Jellyfin.Database.Implementations\\Jellyfin.Database.Implementations.csproj": {
                 "projectPath": "E:\\Projects\\pgsql-jellyfin\\src\\Jellyfin.Database\\Jellyfin.Database.Implementations\\Jellyfin.Database.Implementations.csproj"
               },
+              "E:\\Projects\\pgsql-jellyfin\\src\\Jellyfin.Database\\Jellyfin.Database.Providers.Postgres\\Jellyfin.Database.Providers.Postgres.csproj": {
+                "projectPath": "E:\\Projects\\pgsql-jellyfin\\src\\Jellyfin.Database\\Jellyfin.Database.Providers.Postgres\\Jellyfin.Database.Providers.Postgres.csproj"
+              },
               "E:\\Projects\\pgsql-jellyfin\\src\\Jellyfin.Database\\Jellyfin.Database.Providers.Sqlite\\Jellyfin.Database.Providers.Sqlite.csproj": {
                 "projectPath": "E:\\Projects\\pgsql-jellyfin\\src\\Jellyfin.Database\\Jellyfin.Database.Providers.Sqlite\\Jellyfin.Database.Providers.Sqlite.csproj"
               }

tests/Jellyfin.Server.Implementations.Tests/obj/project.assets.json

@@ -3405,6 +3405,7 @@
           "Jellyfin.Controller": "10.12.0",
           "Jellyfin.Data": "10.12.0",
           "Jellyfin.Database.Implementations": "10.11.0",
+          "Jellyfin.Database.Providers.Postgres": "1.0.0",
           "Jellyfin.Database.Providers.Sqlite": "1.0.0",
           "Jellyfin.Model": "10.12.0",
           "Jellyfin.Sdk": "2025.10.21",

tests/Jellyfin.Server.Implementations.Tests/obj/project.nuget.cache

@@ -1,6 +1,6 @@
 {
   "version": 2,
-  "dgSpecHash": "skyqcPUFzNM=",
+  "dgSpecHash": "wBLLsvDPe+0=",
   "success": true,
   "projectFilePath": "E:\\Projects\\pgsql-jellyfin\\tests\\Jellyfin.Server.Implementations.Tests\\Jellyfin.Server.Implementations.Tests.csproj",
   "expectedPackageFiles": [