Cobalt drills are an excellent compromise. Harder the HSS drills, less brittle than Tungsten Carbide but can still be sharpened to extend their usable life. Expensive but probably worth the investment if you can afford them.

Metric M42 8% Cobalt Twist Drill Bits Set for Stainless Steel and Hard Metal (1mm-10mm/19pcs)
4.0

Bosch Professional 2608587014 19-Piece HSS-Cobalt ProBox Metal Drill Bit Set (for Stainless Steel, Accessories for Drill Drivers), Gold, 1mm-10mm
5.0

HPMAISON True 5% Cobalt Drill Bit Set, 13Pcs M35 High Speed Steel Twist Drill Bits 1.5mm-6.5mm, 135° Split Point Extremely Heat Resistant for Stainless...
4.0