Unfortunately, you can't always understand what I mean
Yes, do you have said this to us (and to me, directly) before.
Our response has been to ask you to consider typing in your own language and allow us to use the translate button. That will likely reduce at least some of the confusion. Or you can persist and continue to explain what you meant, until we do understand what it is you are asking—your choice. Please be patient with us, as we will be with you. We are volunteers—we are not paid staff—instead we are experts in our field and we choose to help others by sharing our knowledge when we have time to spare.
What is it you want the line underneath the header row to look like? Thin like the others, or invisible? Either way, Uwe has already provided the correct answer: define the line under the header row in the cell style.
I understand your words: "use the table style to directly control the thickness of the line" but we have to work with InDesign's feature set. You can control the line under the header row by modifying the header row cell style definition, just like Uwe said. An empty text box does not mean zero—it means leave it as is—you need to define a value if you want to change what it looks like. Once you do, assigning the table style will take care of it.
And as for the "The lower line of the header cell is 0.25mm by default? I didn't set this number, I don't need it"—this is an override. Overrides can float in from Word, from Excel or assigned in InDesign (intentionally or unintentionally). To restore the table to the default settings for that file (and your file has table overrides already in place so it will go back to your defaults, and not InDesign's defaults), select it and Alt/Opt click on [Basic Table], [None] and [Basic Paragraph]. I do this routinely before starting to format any table. If you are interested, you can learn more about how InDesign handles defaults here: https://www.rockymountaintraining.com/adobe-indesign-setting-and-removing-defaults/.
I wish you the best, @dublove.
~Barb
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