I'm not sure why anyone would choose varchar for a column in 2026 unless if you have some sort of ancient backwards compatibility situation.
Dapper has a static configuration for things like TypeMappers, and you can change the default mapping for string to use varchar with: Dapper.SqlMapper.AddTypeMap(typeof(string),System.Data.DbType.AnsiString). I typically set that in the app startup, because I avoid NVARCHAR almost entirely (to save the extra byte per character, since I rarely need anything outside of ANSI.)
Or, one could use stored procedures. Assuming you take in a parameter that is the correct type for your indexed predicate, the conversion happens once when the SPROC is called, not done by the optimizer in the query.
I still have mixed feelings about overuse of SQL stored procedures, but this is a classic example of where on of their benefits is revealed: they are a defined interface for the database, where DB-specific types can be handled instead of polluting your code with specifics about your DB.
(This is also a problem for other type mismatches like DateTime/Date, numeric types, etc.)
It ought to be smart enough to convert a constant parameter to the target column type in a predicate constraint and then check for the availability of a covering index.