I can confirm the Lighthouse problem with Joomla 4.1.2.
But, about the "Tables and lists" problem (missing UL or OL), i think it's a detection problem.
I see this code generated in my 4.1.2 website with the standard mod_languages:

<div class="mod-languages">
  <ul class="lang-inline">
    <li dir="ltr">
      <a href="#it">IT</a>
    </li>
    <li class="lang-active" dir="ltr">
      <a href="#en">EN</a>
    </li>
  </ul>
</div>

I forgot to mention explicitely:

1. I am using Cassiopeia
2. the generated HTML is the following

<div class="mod-languages">
    <p class="visually-hidden" id="language_picker_des_195">
        Sélectionnez votre langue
    </p>

    <ul role="listbox" aria-labelledby="language_picker_des_195" class="mod-languages__list lang-inline">
        <li class="lang-active">
            <a aria-current="true" role="option" aria-label="Français (FR)" href="https://www.mydomainname.com/fr/">
                FR
            </a>
        </li>
        <li>
            <a role="option" aria-label="English (UK)" href="/en/"> EN </a>
        </li>
        <li>
            <a role="option" aria-label="Nederlands" href="/nl/"> NL </a>
        </li>
    </ul>
</div>

Remove the role="option" A link should not change it's role (unless someone is doing it on purpose. Also it should be wrapped in a nav element as it is essential navigation and last the role="listbox" is also wrong

What about this solution: https://russmaxdesign.github.io/language-switcher/

And how would that work if you have 4 or more languages

I don't understand the question... We have 2 options now: dropdown or horizontal list. I'm talking of replacing the horizontal list with the radio buttons. It is semantically correct and the user can navigate through the option with the arrow keys, what is correct. Making keyboard navigation inside the list is much more complicated: https://w3c.github.io/aria-practices/#kbd_general_within

But it is only a suggestion I found as reading more about this topic.

@dgrammatiko is correct about the role being incorrect. please test #37483

I don't understand the question... We have 2 options now: dropdown or horizontal list.
I'm talking of replacing the horizontal list with the radio buttons. It is semantically correct and the user can navigate through the option with the arrow keys.

Just to clarify in case anyone thinks about these things ...This is really wrong for a website frontend.
The "language" switcher must renders links with a real URL that can be indexable by search engine, or will break the whole multilanguage SEO, bacause you loose destination urls to the other languages.
A "language switch" is not a UI interaction like in an APP or in "admin backend", but it's a navigation to a new url.
Google says "Consider adding hyperlinks to other language versions of a page" in the SEO guidelines.
(in fact we no longer use language dropdown on SEO and UX driven websites, it is an anachronistic thing)

The current markup is fine - just the additional roles that were added that is wrong. #37483 corrects that

@simbus82 thank you for the explanation, you are right, I didn't take the links in account... doing too much things at the same time is not a good idea ;-)

Closing as we have a PR #37483