This thread is resolved. Here is a description of the problem and solution.
Problem: Client wants to show visitors the login page in two languages and send welcome emails in both language, but the WP core function is not able to support this. Solution: There is a workaround by using a custom front or login page with a different URL for each language which contains a translatable login form. This way, once on the customized and translated page, the (translatable) login form included in that page will show admin texts and send admin mails in the language assigned to the page. Relevant Documentation:
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