Hi,
I don't see why that would happen.
And if you click somewhere else on the page does the virtual keyboard closes itself ? (it should I suppose)
Also, you say it works on Joomla 4. So I doubt the issue is in HikaShop since I suppose you've tested with HikaShop custom item fields on joomla 4.
Did you try with the same template on Joomla 4 ?
If yes, then it means it's not coming from the template either.
If not, could you do that test ?
It could also come from a plugin or a module adding it's javascript to the page and somehow messing the behavior of that "done" button. so that might be why you don't have the issue on Joomla 4 as you don't have these extra modules/plugins
Also, do you have the issue on other forms like on this page ?
jouwnaambord.nl/bedrijfsnaambord/offerte-bedrijfsborden
If yes, then it means that it comes from something which is on all the pages.