Two sources of information that suggest the answer is 3", though none of these are IBC / IRC. Still, in the absence of actual code definition, some AHJs might accept alternate interpretations like these. The ADA diagram touches on the "overhead projection" discussion in a fair straightforward way. Give that a blind person might need to sweep their hand vertically to find the rail, any sharp-edged obstructions right above the rail seems like a good way to bruise your knuckles. California Building Code 2022 (Vol 1 & 2) > 11A Housing Accessibility > 1115A Exterior Stairways > 1115A.6 Exterior Stairway Handrails:
1115A.6.2.4 Handrail Projections
Handrails projecting from a wall shall have a space of 11/2 inches (38.1 mm) minimum between the wall and the handrail.
Handrails may be located in a recess if the recess is a maximum of 3 inches (76.2 mm) deep and extends at least 18 inches (457 mm) above the top of the rail. Any wall or other surface adjacent to the handrail shall be free of sharp or abrasive elements. (See Figure 11A-6B.)
https://www.ada.gov/law-and-regs/design-standards/1991-design-standards/#426-handrails-grab-bars-and-tub-and-shower-seats Handrail. Handrail is mounted into a recessed section of a wall. The bottom of the recessed section is not more than 3 inches wide where the handrail is located. The recessed section shown extends vertically approximately 6 inches and then angles to a point on the flush wall a minimum of 18 inches (455 mm) above the grab bar. This profile is provided to permit grasping from a standing position. Spacing between handrail and the adjacent wall shall be 1- 1/2 inches (38 mm). Handrail shall be 1-1/4 to 1-1/2 inches diameter (32 - 38 mm). Support for the handrail is from below.
