it is not a sub-directory of the domain where the wordpress installation is located. the sub-directory is in public_html and rewrite rule is being used to point to the sub-directory directly. so, it is not supposed to affect the domain at all.
https://domain.com is pointing directly to [domain.com] folder inside public_html. it is NOT pointing to public_html with wordpress files in [domain.com] folder as you thought. So, https://example.com/example.com/ is irrelevant.
Which part of the webpage that you provided you wanted me to see actually?
Method I is exactly what I was doing before and as it was written at the end of Method I section, that’s all need to be done. Nothing else. URL change in database and wp-config is not needed.
But if you read my previous message carefully. The issue is not on having the website visible. It is the redirection URL from wp-admin login.