The Adherent of Ancient Osirion
"Although Bastet has been all but forgotten by the native Osirians, you either sojourned with or were raised in a cult dedicated to the cat-headed goddess of Ancient Osirion. You treat the tekko-kagiUE as a martial weapon instead of an exotic weapon. You also treat the tekko-kagi as if it were a set of claw blades when determining how it interacts with other effects."
What effects are the special effects to claw blades it is referring to?
The Claw blades reads
"The blades grant the wearer a +1 enhancement bonus on claw attack rolls with that hand and change the weapon type from a natural weapon to a light slashing weapon. Catfolk with the cat’s claws racial trait are proficient with this weapon. The claw blades can be enhanced like a masterwork weapon for the normal costs. The listed cost of the item is for one set of five claws for one hand."
They might have made it with the Idea that there would be more claw blade specific abilities in the future.
The only thing I've found so far this would affect would be the catfolk specific monk FCB to treat claw blades as a monk weapon, use style strikes with it and add 1/2 damage to it. That trait would allow tekko-kagi.
Catfolk using claw blades (& tekko-kagi with that trait) can use them with effects intended for their claw natural attacks, like the claw pounce feat. I think there's a spell or two and maybe another feat this can effect as well.
Like Feral Combat training, and Style feats?
Where is that rule? That would be great to have
You quoted it. 'The blades grant the wearer a +1 enhancement bonus on claw attack rolls with that hand and change the weapon type from a natural weapon to a light slashing weapon.'
They're still claw attacks, and claw pounce just specifies that you use your claws, not that it requires a natural weapon. Feral combat training does specify natural attacks and wouldn't work. There are a few styles which use weapons but most wouldn't work.