Drilling a hard material needs a drill harder than the material being drilled.
In the 18th century, not much choice – either the very best carbon steel they could get find and lots of patience and resharpening, or maybe carborundum or diamond. The usual method was to dodge the problem by drilling any holes needed when the steel was still soft. Hardened steel is usually worked by grinding, not by cutting.
Softening spring steel, drilling, and re-hardening is an option but making springs is skilled work. I'd want plenty of successful practice behind me before risking an antique clock, or at least an alternative if I ruined the original part. (An old time clockmaker would keep a few apprentices busy making parts. If anything broke, they'd be beaten soundly and told to do it again. Cost a fortune, which is why later clockmakers increasingly used parts bought in from specialists.)
Today we have more drills suitable for hard drilling, not cheap though! Whatever type is used, lots of pressure and cutting oil are needed. TiN coated HSS or Cobalt drills stand a chance but no tears if a few get destroyed in the process. Solid tungsten drills are perhaps the most affordable approach, but hard means brittle: thus any operator error means an expensive breakage. (A Karnasch 4mm K-Drill Solid Carbide Drill for Hardened Steels is nearly £70 from Cutwel.) Never researched the cost of really high-end drills like Boron Nitride, I guess they're even more pricey.
Spark erosion works but equipment needed and deep holes are a challenge. Acids make untidy holes.
Dave