Search on part of a column in a SQL Server cross-database view
Are you allowed to replicate that table in another database? Using transactional replication, for latest data access. If yes, then I'd test a more cumbersome process like replicating the needed table, building another table or materialized view with a computed column as you need.

If replication is not an option, I'd say that you need to establish a scheduled process to take that table in your database and continue locally to process the data. Exactly like the first suggestion, but using your own scripts and schedule.

That, or I think you're stick to the scalar functions that aren't really the best option from performance point of view.