chore: update changeset and implementation

Signed-off-by: blam <ben@blam.sh>

.changeset/pink-pets-jump.md

@@ -2,4 +2,4 @@
 '@backstage/backend-defaults': patch
 ---
 
-Support `client: pg+google-cloudsql` in database client for usage with `@google-cloud/cloud-sql-connector` and `iam` auth
+Support `connection.type: cloudsql` in database client for usage with `@google-cloud/cloud-sql-connector` and `iam` auth

packages/backend-defaults/src/entrypoints/database/DatabaseManager.ts

@@ -252,7 +252,6 @@ export class DatabaseManager {
         databaseConfig,
         {
           pg: new PgConnector(databaseConfig, prefix),
-          'pg+google-cloudsql': new PgConnector(databaseConfig, prefix),
           sqlite3: new Sqlite3Connector(databaseConfig),
           'better-sqlite3': new Sqlite3Connector(databaseConfig),
           mysql: new MysqlConnector(databaseConfig, prefix),