I have a shopify store setup with two regional domains, which using hreflang tags as populated by shopify. However when doing a website audit (Link Assistance Website Auditor) I get the error:

'It appears that some pages with hreflang elements either miss self-links or have no return-links from other language versions of a page. '

But I can't see the issue, and am wondering if anyone can help. Below is the example concerned from my head section (the second domain is just the account domain for shopify)

<link rel="alternate" hreflang="x-default" href="https://www.website.com.au/collections/shirts"><link rel="alternate" hreflang="en" href="https://website.myshopify.com/collections/shirts"><link rel="alternate" hreflang="en-NZ" href="https://www.erilan.co.nz/collections/shirts"><link rel="alternate" hreflang="en-AU" href="https://www.erilan.com.au/collections/shirts">

I'm using shopify's 'local domains' feature, which essentially gives me several domains as hreflang tags with the relevant '<link ref="alternate"> hreflang tag on each page showing the various language/country options. But I've noticed that the sitemaps generated don't include alternate links, but are available at every domain. So for example www.website.com.au/sitemap.xml gives australian links while www.website.co.nz/sitemap.xml gives new zealand links.

My questions are:

1)Should the sitemaps themselves include the alternate links for each page? This page from google suggests it should but I can't tell if that's in place of having it defined as hreflang tags on the page itself.

2) Should I instead create a second Google Search Console account for the alternative domain and submit the alternate sitemap there or is there a way to do it within the one account?

Thanks!