Hi,
Since the test email is working, it's probable that HikaShop is sending the emails too but they get blocked for some reason.
Go in the menu Customers>Emails history in your HikaShop backend.
There, you'll see a list of all the emails sent by HikaShop.
If the emails are not there, then HikaShop didn't send the emails and it's probably because they are disabled in the System>Emails menu.
If the emails are there, then HikaShop did send the emails to the email server. In that case, if the email is not received by the receiver, an error will be logged in the log of the email server of your hosting. So in that case, you should contact your hosting support with a copy of the email information from the email history in HikaShop so that they can check the log for the error message.
Also, it's likely that the cause is linked to spam. Your emails are probably being catched by a spam filter and discarded because of that. So I would also recommend to test these emails with
www.mail-tester.com/
to see what's wrong with them.