Unlikely.
Closest to what you have that I've ever worked on is a set of 4ea 3 MV 11kV diesel gensets on oil platform.
No 'surge suppressors' on those generators.
Most similar I ever saw to what you describe (no load) was due to a cracked bushing which allowed corona (PD if you prefer that terminology) in the crack area which spread to the contact when switch opened, phase to phase.
I'd do a close inspection of the cup bushings on your switches.
Next closest example was due to a loose fast-on (spade lug) connection to a Basler regulator that allowed an overvoltage transient (found as we had difficulty bringing that gen on line with the other gen under load). Why anyone would ever mount anything with fast-on connections on a gen set is beyond me, but we see mfg. doing it all the time.
