fix(ha): PostgreSQL migration backup no-op + URI connection string support

- MigrationBackupFast/RestoreBackupFast/DeleteBackup return no-ops for
  PostgreSQL; pre-migration backups are handled by jellyfin-pg-backup
  CronJob, not the automated backup path that throws NotSupportedException

- ServiceCollectionExtensions: detect postgresql:// / postgres:// URI
  format in POSTGRES_CONNECTION_STRING and convert to ADO.NET key=value
  format before passing to NpgsqlDataSourceBuilder (which requires it)

Closes startup crash: 'Automated migration backups are not supported for
PostgreSQL' on first boot with a fresh database.

Jellyfin.Server.Implementations/Extensions/ServiceCollectionExtensions.cs

@@ -149,6 +149,23 @@ public static class ServiceCollectionExtensions
                         "No PostgreSQL connection string found. Set the POSTGRES_CONNECTION_STRING environment variable, " +
                         "or provide it via CustomProviderOptions.Options[\"ConnectionString\"] or CustomProviderOptions.ConnectionString.");
 
+                // Support postgresql:// / postgres:// URI format (e.g. DATABASE_URL convention).
+                // NpgsqlDataSourceBuilder requires ADO.NET key=value format; convert if needed.
+                if (connectionString.StartsWith("postgresql://", StringComparison.OrdinalIgnoreCase)
+                    || connectionString.StartsWith("postgres://", StringComparison.OrdinalIgnoreCase))
+                {
+                    var uri = new Uri(connectionString);
+                    var userInfoParts = uri.UserInfo.Split(':', 2);
+                    connectionString = new NpgsqlConnectionStringBuilder
+                    {
+                        Host = uri.Host,
+                        Port = uri.Port > 0 ? uri.Port : 5432,
+                        Database = uri.AbsolutePath.TrimStart('/'),
+                        Username = userInfoParts.Length > 0 ? Uri.UnescapeDataString(userInfoParts[0]) : null,
+                        Password = userInfoParts.Length > 1 ? Uri.UnescapeDataString(userInfoParts[1]) : null,
+                    }.ToString();
+                }
+
                 var dataSourceBuilder = new NpgsqlDataSourceBuilder(connectionString);
 
                 dataSourceBuilder.ConnectionStringBuilder.MinPoolSize = GetPoolOption(options, "MinPoolSize", 2);

src/Jellyfin.Database/Jellyfin.Database.Providers.PostgreSQL/PostgreSqlDatabaseProvider.cs

@@ -15,8 +15,9 @@ namespace Jellyfin.Database.Providers.PostgreSQL;
 [JellyfinDatabaseProviderKey("Jellyfin-PostgreSQL")]
 public sealed class PostgreSqlDatabaseProvider : IJellyfinDatabaseProvider
 {
-    private const string BackupNotSupportedMessage =
-        "Automated migration backups are not supported for PostgreSQL. Use the jellyfin-pg-backup CronJob for nightly S3 backups.";
+    // Sentinel returned by MigrationBackupFast to signal that no file backup was
+    // created (PostgreSQL backups are handled externally by jellyfin-pg-backup CronJob).
+    private const string NoAutomatedBackupKey = "postgresql-no-automated-backup";
 
     private readonly NpgsqlDataSource _dataSource;
 
@@ -69,19 +70,24 @@ public sealed class PostgreSqlDatabaseProvider : IJellyfinDatabaseProvider
     /// <inheritdoc/>
     public Task<string> MigrationBackupFast(CancellationToken cancellationToken)
     {
-        throw new NotSupportedException(BackupNotSupportedMessage);
+        // PostgreSQL pre-migration backups are handled externally by the
+        // jellyfin-pg-backup CronJob. Return a sentinel so callers know no
+        // file backup was created and the migration can proceed safely.
+        return Task.FromResult(NoAutomatedBackupKey);
     }
 
     /// <inheritdoc/>
     public Task RestoreBackupFast(string key, CancellationToken cancellationToken)
     {
-        throw new NotSupportedException(BackupNotSupportedMessage);
+        // No automated backup was taken; nothing to restore.
+        return Task.CompletedTask;
     }
 
     /// <inheritdoc/>
     public Task DeleteBackup(string key)
     {
-        throw new NotSupportedException(BackupNotSupportedMessage);
+        // No automated backup was taken; nothing to delete.
+        return Task.CompletedTask;
     }
 
     /// <inheritdoc/>