You should be able to restrict suggestions for certain schema's in SQL Prompt Options by using Connections -> Specifiy the databases you want to load suggestions for:
This should only load suggestions for the schema's you specify, and then load suggestions for the objects in those schemas.
Here is our documentation on how to use this option: https://documentation.red-gate.com/sp/managing-sql-prompt-behavior/managing-connections-and-memory#Managingconnectionsandmemory-ManagingdatabaseconnectionsManagingdatabaseconnections
I hope this helps.
The arrows only affect how object names are displayed in the suggestions box. The schema (owner) name is only inserted into your code when Qualify object names with owner name is selected on the Inserted Code > Qualification options page.
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