If you go to Tools -> Site Health, do you see a message about “One or more recommended modules are missing” that includes “xml”? If so, you can have the host look at my info for re-enabling it: https://www.mail-mechanic.com/woocommerce-email-formats#fix-unavailable-html

If that doesn’t seem to apply, you could rule out whether it was an issue with WooCommerce or the host/WordPress by sending a test HTML email with something external to WooCommerce. WP HTML Email works for that (https://wordpress.org/plugins/wp-html-mail/) or there’s probably others.

If that doesn’t provide any clues, can you post your system report (https://wordpress.org/support/topic/before-posting-gather-the-following-details/)? And ideally describe how the mail is sent (through the default mail-sending on the web server, through SMTP, etc.). Maybe I’ll spot something from that.

Are you using the host for email? If so, I’d suspect the problem is on their end rather than being anything related to your WordPress install. You could ask them to troubleshoot, but just switching to a dedicated email provider would probably solve the problem, and usually gives better deliverability rates than the usual poorly-configured host mail. And they’re usually free/cheap for low email volumes. There’s the list of them in the email FAQ, and I’m working on a more comprehensive list.

If you’d like to distinguish between WordPress problems and host problems, you could upload a basic PHP file to your account that just calls the mail function with an HTML body / headers. If it worked correctly, you’d know the problem was on the WordPress side, and if it still failed, you’d have an easy test case for the host.