Is there a possibility to change the Domain Field Values after saved in the QGIS geopackage?
How can I add e.g. Type 4 to the Values after saving the domain?
It's possible to modify the domain after creation but it's not straightforward, in your exemple it will probably be simpler to just delete the domain and recreate it. That being said, to modify a GPKG domain you need to modify the table that store the domain information, to do that :
Make a copy of your GPKG as a backup if something go wrong
in QGIS open the DB manager (in the menu : Database > DB manager or add the database toolbar and click on the database icon)
In the provider panel of the BD manager right click on SpatiaLite and choose "New connection..." then navigate to your geopackage and select it. You want to add a SpatiaLite connection rather than the more logical GeoPackage connection to be able to look at system table. The procedure will work the same if you add a GeoPackage connection, you just wont be able to check table or field name or to see what your domain currently look like.
Select the connection corresponding to your geopackage and open the SQL window (menu : Database > SQL Window or click on the wrench icon)
To add a new domain value (in your exemple 'Type 4') enter the following SQL and click the Execute button
INSERT INTO "gpkg_data_column_constraints" (constraint_name, constraint_type, value, description) values ('Type', 'enum', 'Type 4', 'Type 4');
or in a more general way
INSERT INTO "gpkg_data_column_constraints" (constraint_name, constraint_type, value, description)
VALUES ('Domain name', 'enum', 'Domain code', 'Domain description');