For design of pilot seat, would the seat be considered as primary or secondary structure?
Seats are not structure. They are equipment.
I believe you mixing system/sub-system definitions with design requirements. Primary and secondary structures are structural systems within the aircraft that have a primary or secondary purpose of transferring a load. Everything else on the aircraft is classified according to its primary function (air conditioning, flight controls, etc.)
Having said that, there are structural requirements that exist for all the components of these functional systems. That doesn't make them structure.
To illustrate the point, we can refer to ATA spec 2200 which provides a common structure for aircraft documentation. The documents use use a Chapter-Section-Subject numbering system that correlates to a System-Subsystem-Subject.
At the highest level, Chapters 20 through 50 cover Aircraft Systems, 50 - 59 cover structure, 60 - 67 cover Propeller/Rotor, and 71 - 84 cover Power Plant. Looking at the Chapter definitions we find (emphasis mine):
Chapter 25, EQUIPMENT/FURNISHINGS
Those removable items of equipment and furnishings contained in the flight and passenger compartments. Includes emergency, galley and lavatory equipment. Does not include structures or equipment assigned specifically to other chapters.
And under that is:
Section -10, Flight Compartment
The compartment above the floor and between the forward passenger partition and the forward pressure dome. Includes items such as flight crew seats, tables, pilot check lists and food containers, wardrobes, curtains, manuals, electronic equipment rack, spare bulbs, fuses, etc. Does not include cargo compartments.
Further along, we find:
Chapter 51, STANDARD PRACTICES AND STRUCTURES - GENERAL
Standard Practices, General Procedures and typical repairs applicable to more than one chapter and are not specifically covered under [Chapter (System) 52] thru [Chapter (System) 57] Sub-Sys/Sect breakdown.
Section -10, General
Airplane major structural breakdown diagram. Primary and secondary structure diagram. Principal area and dimensional data. Restricted area diagram. Zoning diagram. Access door and panel identification. Glossary.
The structural area of interest here is:
Chapter 53 FUSELAGE
Structural units and associated components and members which make up the compartments for equipment, passengers, crew, cargo, plus the structure of the envelope and gondola of airships. Includes skins, belt frames, stringers, floor beams, floor, pressure dome, scuppers, tail cone, fuselage-to-wing-and empennage fillets, attach/attached fittings, load curtains, cables, ballonets, etc.
You'll note that this specifies only physical structure, not systems or equipment installed in the fuselage.
To address the structural design requirements, we can refer to 14 CFR Part 25, Airworthiness Standards: Transport Category Airplanes.
Subpart C with the title Structure is broken down into the loads the aircraft must be designed to withstand (flight loads, gust loads, ground loads, etc.)
Subpart D covers Design and Construction which provides specifics for individual design elements of the aircraft. Therein we find:
§25.785 Seats, berths, safety belts, and harnesses.
Within this section is the necessary design requirements for seats, etc. which reference the applicable load specifications of Subpart C. A detailed reading of this section will reveal that the design loads for the seats are driven by the Emergency Landing Loads defined in Subpart C.
That falls under the subject of Flight Deck and Furnishings. The Airline Transport Association (ATA) classifies that equipment under Chapter 25 Equipment and furnishings. OEMs as well separate that equipment from structural airframe components as well. Primary and secondary structures refers to structural components in an airframe.
For example, a fwd wing spar or a fwd pressure bulkhead are primary structures.
A Douglas clip might be an example of a secondary structure, etc.