no, there is no such thing as bestiality in this series, it's only used as a mix of comedy but also to insist on the fact the duchy's vassals really went too far trying to cross bred their lord, just like she said in this chapter (my POV: and from the pregnant maid we saw, it's more like one of the vassal was trying to have another baby take over the title of grand duke for themselves, probably by having said maid lie and pretend that it was the grand duke's...). Else, as you can see in these latest chapters, she is pretty much treating him as a big dog she needs to tame. At one point, she will kiss him once, think any pet owner kissing their puppy's lightly, and he will turn back into being a human (a magical kiss!!... from someone who was a witch in their past life ^^;
. There is someone in the forum spoiler thread of this series on novelupdates who wrote that she will need to kiss him every 12h for him to keep his human shape, but to take it with a grain of salt since they were not totally sure about that information.