Is the APU classified as a component of Airframe or Powerplant?

In the U.S., auxiliary power units are categorized under Powerplant for the purposes of maintenance. The FAA Aviation Maintenance Technician Handbook - Powerplant, Volume 1 lists auxiliary power units in the category of turboshaft engines on page 1-38.

I was a tech writer in another life. Under ATA100/2100, the Air Transport Association system of categorization of systems for maintenance manuals, the APU is Chapter 49 (Airborne Auxiliary Power).

Power Plant chapters are 70 and up. (Some OEMs also use a equivalent numbering convention for engineering drawings to align them to ATA100/2100, where, say, if Flight Controls are Chapter 27, flight controls related drawings would have "27" at the start of the drawing number with the applicable sub-system numbering as appropriate - makes finding drawings in a database quick and easy).

Airframe systems are Chapters 20 thru 50. So from that standpoint, its Chapter 49 designation makes the APU an airframe system, not a Powerplant (which only refers to propulsion engines per ATA), as far as the industry is concerned, and I think you are pretty safe to go on that.

It is a "power plant", so it would be classified as such. An APU isn't much different than a small jet engine.