Hi,
If the email is in the email history, then the email was sent to the SMTP server of your hosting and it accepted it. So, from that point, HikaShop did its job.
However, if the email was not received, it's likely that it got blocked somewhere.
I would first recommend trying your registration with
mail-tester.com/
in order to check if everything is properly setup and if your server is not on some kind of blacklist.
Also, the exact reason why the email was not delivered to the recipient mailbox is normally logged in the log file of the email server of the hosting. So you can contact them with a screenshot of the details of an email that was not received from the email history and ask them to look into the log of the email server for the reason why the email was not delivered. They should be able to tell you what's wrong.
If it's not a spam issue (which you can check with mail-tester) it's usually a problem with what you configured under the "emails" section of the HikaShop configuration. So you can also provide a screenshot of this to your hosting support.