Is is limited to the emails sent on account registration or do other email notifications also fail to work? If it's only the validation emails I would guess the problem is likely not that the emails are not sent but rather they get blocked on their way or end in spam folders. If it's all email notifications it's likely a matter of mails not getting send indeed.

Is it necessary to use a SMTP plugin? If your server also has a mailserver, it should be possible without any additional plugins. If the mailserver is not configured, you might want to ask the webhoster support to help you with the configuration. You should then also be able to create a mail address on your domain that you can use as site email address.

If using SMTP the problem might also be with the site email address in case its domain does not match the domain of the SMTP mail server (mail providers will likely not allow sending mails over their servers with other domains used in the from address). Unfortunately, I've no idea what else might be wrong with SMTP email sending as I never did that myself. Maybe it's just the plugins you use are not fully compatible with the latest Elgg versions anymore.