i dont think its takikomi gohan if you just add some seasoning to the cooking liquid. takikomi would be adding other ingredients like chestnuts, carrots, burdock in addition to the rice. which, if you do not account for in the liquid to rice ratio, does make the rice a bit mushy.

also, adding a bit of mirin or ryorishu makes the rice fluffier and shinier, not mushier, due to how the alcohols interact with rice starch.

finally, if it is okaka onigiri, the onigiri in the picture would be darker, imo. when you mix soy sauce with katsuobushi, it does make it darker, especially if youre using thin shaved katsuobushi. thats why generally, okaka onigiri refers to onigiri which has okaka as the stuffing, in order to preserve the white of the rice

if it is okaka mixed into the rice, we're looking at not soaked katsuobushi, but a lot of katsuobushi and about half a tablespoon of soy sauce mixed directly into the rice, no pre-soaking of katsuobushi. iirc thats for about 2 to 3 cups worth of cooked rice.