as far as I understood... you have implemented partioning on an existing table with existing structure... so everything existed and you "just" splited it up into several partitions.
You have to tell those additional indexes also that they are based on a partition to perform accordingly!
Actually all those "old" indexes don't know anything about those partitions, you have to tell them that there is something going on ;-)
Here is an example:
https://learn.microsoft.com/en-us/sql/t-sql/statements/create-index-transact-sql?view=sql-server-ver15#j-create-a-partitioned-index
Hope this helps you to understand how to proceed.