Thinking of God’s Name in Shower

It is my understanding that saying out loud Hashem’s names (any of them ) in the bathroom is a moderate-medium violation of the Torah, because it is demeaning and derogratory (disrespectful) to God, simply because of the context includes the using of the toilet, for example. And I understand the part about the fact that it doesn’t matter that a sink and a shower or bathtub might be there. But what is the general consensus Halacha ruling on the “thinking” about G-d IF the thinking occurs during the our cleansing inside thew shower or bathtub? Is it permissible or not?

And secondly, does it make a difference if the so called “thinking” is done in a bathtub whereby we remain in the part-filthy part-soapy water as opposed to a shower where we are in a state of constant cleansing?

Given the long history of the importance of remaining ritually clean, I should think that that the Halacha (including Mishna and Gomorra) would have extensive commentary on this matter and that silent thinking about G-d (for example, a posed in the written Torah or his will in general, or Hashem’s relationship with Moshe and the Moshiach) is acceptable, on strict condition that the toilet is not being used in any way.

Please explain in detail as much as possible. Thank You and Be Well.