The hit list configuration is saved per user or as common hit list confiuration. The common hit list configuration is used as default, if the user has not specified a special hit list configuration.
I would advise to export and import the common hit list configuration. For this you can use the dms-service rest-api endpoint UserService.getResultListConfiguration with mode COMMON for export on the source system and the endpoint UserService.saveCommonResultListConfiguration for import on the target system. This can be done for each type and context type combination.
There is currently no system provided method to export and import all hit list configurations for all available types.