There is function "Referenced Cost Centers" in App Manage Activity Type Master Data. It's not clear what action will update this list.
SAP S/4HANA Cloud
Reproducing the Issue
Check function "Referenced Cost Centers" in App Manage Activity Type Master Data.
See Resolution part.
You should use App Manage Activity Types (Version 2) for activity relevant processing, since this is the latest one.
The "Referenced Cost Center" function is replaced by "Where Used" function in App Manage Activity Type Master Data. There, you can find the similar outputs.
Regarding the entries in Sending Cost Centers (in Cost Rate Maintenance), it will be updated if you maintain plan cost rates with App Manage Cost Rates - Plan. It's not useful to extend the To Period and To Year for the cost rates. The From Period and From Year matters here.
For example, if you maintan a cost rate with From Period = 1 and From Year = 2021, you will find year 2021 is inserted in the list.
Activity type, valid period, F1605A , KBA , CO-FIO , Fiori UI for Overhead Cost Controlling , Problem