Hi,
It indeed happened with the update but it comes from something else.
The issue is that the hikashop.js file is removed from the HTML header of your pages and that should not be done.
I don't know if it's something you removed yourself, or if you have an extension (or your template) removing that javascript file, but it is necessary for any page displaying HikaShop.
Before the contact page didn't need it but now that the contact page supports custom fields, a javascript error will happen if that javascript file is missing and that's why the contact form doesn't work.
So you need to either fix or disable the extension causing the issue.
Try to switch temporarily your joomla template with the default one of Joomla and see if you still have the problem. If not, then it's a problem with the template and you should contact your template provider.
Otherwise, try the same procedure with each system plugin.