However, it also adds the link tag for the current language.

I agree that seems to be wrong/bug

Correction after looking at the spec it has to exist on all the languages see https://developers.google.com/search/docs/specialty/international/localized-versions#common-mistakes

Main issue here is that when "Add alternate meta tags" is on yes, it makes the canonical tag disappear

Main issue here is that when "Add alternate meta tags" is on yes, it makes the canonical tag disappear

as it should

So it's expected to not have the alternate href of the other language when you have the canonical URL tag?
On another site, both the canonical tag and the href tags are there. I'm lost

The canonical tag in joomla refers to a canonical domain not a canonical url

rel=alternate is like saying that the url is a soft canonical url for that language

Easier if I explain with an example.

I'm supposed to have in my source code:

<link href="https://xxx.com/collection/lady-datejust/lady-datejust-279138rbr-0015" rel="canonical">
<link href="https://xxx.com/collection/lady-datejust/lady-datejust-279138rbr-0015" rel="alternate" hreflang="en-US">
<link href="https://xxx.com/fr/rolex/collection/lady-datejust/lady-datejust-279138rbr-0015" rel="alternate" hreflang="fr-FR">

But I have this:

<link href="https://xxx.com/collection/lady-datejust/lady-datejust-279138rbr-0015" rel="alternate" hreflang="en-US">
<link href="https://xxx.com/fr/rolex/collection/lady-datejust/lady-datejust-279138rbr-0015" rel="alternate" hreflang="fr-FR">

After doing some tests, I noticed that if I disable Add Alternate meta tags, the canonical link is back (but of course it's not a solution).

However, it also adds the link tag for the current language.

I agree that seems to be wrong/bug

Correction after looking at the spec it has to exist on all the languages see https://developers.google.com/search/docs/specialty/international/localized-versions#common-mistakes

Note that what is written there is not the same. What it says is that if [page EN] has a hreflang tag to [page FR], then [page FR] has to have a hreflang tag to [page EN]. I completely agree with this.

The problem pointed at here is that [page EN] has a hreflang tag to [page EN] (itself), which also has the side effect of removing the canonical tag.

I think I found the solution to this issue. The line:
if($i !== $this->current_lang)
needs to be added before the line:
$doc->addHeadLink($server . $language->link, 'alternate', 'rel', ['hreflang' => $i]);
in the file plugins/system/languagefilter/src/Extension/LanguageFilter.php

That way, the language filter plugin will skip adding the hreflang tag for the current language and only add it for other languages.

and that would be wrong as stated before at the link I shared from google

If page X links to page Y, page Y must link back to page X.

Or have I misunderstood that statement?

I agree with that statement. But we're not talking about this here.
The problem I'm talking about is that at the moment page x is linking to both page x and page y, and that page y is linking to both page x and page y.
My proposed change make it so that page x only links to page y, and that page y only links to page x.
I hope it is more clear.

Note that we found the solution to this problem:
https://www.hikashop.com/forum/product-category-display/907095-issue-ith-canonical-urls.html#356157
It's been tested for several weeks and after this change, everything works as expected.

Hi @hikashop-nicolas - thank you for your contribution - would you like to do a PR for the fix in Joomla? Otherwise i can do it.

Hi, and thanks for coming back to it.
Please make the PR if you can. I don't have the setup on my local machine to do it easily.

My Research has shown that it is recommended to have the link tag with rel="alternate" hreflang="en-US" even on the page with the same language (self referencing) and even if there is a canonical tag, but only if translated pages exist. My tests showed that if you have a canonical tag, the hreflang tag is gone, which seems to be wrong. @hikashop-nicolas: I don't think your solution is correct.

Yes, the solution I proposed is to keep the canonical tag and not add the self referencing hreflang tag to avoid overriding the canonical tag. If you want to keep both, that's indeed not the solution you want.

A solution to be able to keep both would require changing the way HtmlDocument is written: https://github.com/joomla/joomla-cms/blob/5.3-dev/libraries/src/Document/HtmlDocument.php
That's because both the canonical URL and the self referencing hreflang tags normally need to use the URL of the current page and HtmlDocument uses the URL of the tag as key of the array. Which means that without changing HtmlDocument, you can't have both tags at the same time on a page.

And changing HtmlDocument to allow for that might have complex backward compatibility consequences because changing the way the _links array is done there means that third party code using setHeadData or mergeHeadData or getHeadData (or even directly using the _links attribute) would need to adapt to the change if they get/set the "links".

I believe my solution would be a nice improvement in the short term as canonical tags are more important than self referencing hreflang tags for SEO.
And in the long term (Joomla 6 ?) a better solution which would break the backward compatibility of HtmlDocument would be even better.
That is unless someone has a better insight of the situation and/or a better solution to propose ?

I will prepare a PR with a separate array in the document for hreflang tags, thus enabling them to be separate of other link tags e.g. having a canonical tag with the same link, will go into 6.0 probably

That's indeed a great long term solution.

Please test #45428. Thanks.