You have configured your account type per roles. However, after adding the account as favorite, in the favorite menu you are not seeing the roles.
"Image/data in this KBA is from SAP internal systems, sample data, or demo systems. Any resemblance to real data is purely coincidental."
SAP Cloud for Customer
The Favorites functionality identify the type of the document, however it does not identify the role of the account.
On Favorites menu the account will not show the role of the account. This is a system behavior.
An alternative option may be to check the SAP Customer Influencer Site to submit an idea on Influence.
Favorites; Account; Role , KBA , AP-RC-UIF , C4C UI Framework , Problem