I use the editor in the browser, which is translated into Czech. This is perhaps the reason for these conflicts. I changed the category of the route to a path for pedestrians and cyclists, which is according to the official traffic signs (C9). The designation "path" is translated into Czech as "footpath" in the editor, so I changed the category without further investigation.
On the other hand, I think that my marking is not wrong, according to the page https://wiki.openstreetmap.org/wiki/Cs:Key:highway#Ostatn%C3%AD_druhy_cest (in Czech) it is better to mark the path more specifically highway=cycleway , in this section the traffic sign is explicitly mentioned as the same as on the spot (C9). If you want to mark it according to your proposal, please do so, but note that perhaps thousands of kilometers of such trails in the Czech Republic are marked in this way, and Kralupy is the only place where I have come across your way of marking.