Oh Thracian gladiator!
If the tappets were
THAT TIGHT

"I checked the valve clearances and they were all set to zero!", I am wondering what the valve seats might look like, or if the piston has been touching the valves!

From what I can find your 0.20mm (0.008") inlet and 0.30mm (0.012") exhaust were quoted on more than one site, but I think that the quoters were getting their mm and inches in a fankle. Then I found an online pdf manual for a GZ250GN that looks very similar to a 250GN. Tell me I'm wrong!
"Valve clearance (when cold):
IN. : 0.03-0.08 mm (0.001-0.003 in)
EX.: 0.08-0.13 mm (0.003-0.005 in)"N.B. THIS IS 0.003" for the inlet and 0.005" for the exhaust that is a lot tighter than you have them now! But, nearer were I would expect the clearances to be on a "soft" cam. I wonder if somebody tried to set the tappets with the engine not set at T.D.C?

Whatever? I wouldn't run it before I had delved into it's guts above the crankcases or got my money back from the "dealer"!
This is the link to the online pdf:
Suzuki-Gz250_manual.pdfI would suspect top end wear, piston slap and or a little end making a racket. So head off, barrel off and see what you have got. May be time to claim "Goods unfit for purpose"!

Sorry to be a pain in the Horlicks. I can only hope that the chariot is not that badly damaged and I am not Erebus!

Good health, Bill