The sauce that is good on Japanese noodles is shoyu or soy sauce, tsuyu "a dashi-based dipping sauce", yakisoba sauce, "sweet, savory and tangy", and even mentsuyu sauce, which is a dashi and soy sauce concentrate.
Other flavorful additions for Japanese noodles are chili oils such as rayu, a simple combination of soy sauce and butter and even chili crisp for a spicy addition.
Starch is what makes sauce stick to noodles.
The starch that makes sauce stick to noodles is released from the pasta into the cooking water as a result of emulsion with the fat and sauce and binds the sauce to the noodles.
To maximize the sauce sticking to the noodles, you should always reserve some starch pasta water before you drain the pasta.
Then finish cooking the pasta sauce over low heat and add the reserved pasta water to create a thicker and cohesive sauce which coats the noodles.
Not using some pasta water for the pasta is a common mistake when making pasta and causes the pasta sauce to not stick to the noodles.
Starch is key in making pasta sauce stick to pasta as the starch in the water acts as a natural glue, which thickens the sauce and helps the sauce adhere to the surface of the pasta.
And when mixed with the fat in the sauce, the starchy water also helps to create an emulsion, which creates a richer and glossier sauce that binds to the pasta.
To get your pasta sauce to stick to the pasta, salt the pasta water as it seasons the pasta and helps to release starch from the pasta into the water.
And aim for slightly undercooked or al dente pasta as it will continue cooking and absorb the pasta sauce in the pan.
And before draining the pasta water, save at least 1/2 a cup of the cloudy starchy pasta water.
Then add the nearly cooked pasta directly into the sauce pan and add a splash of the reserved pasta water and stir or agitate the mixture to help the starch and the sauce and fat combine.
And keep tossing the pasta in the sauce over low heat until the pasta sauce is a thick and glossy cohesive coating.