Just as an update:
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I’m unable to use Google’s search-console because I am using a stock ynh.fr domain. As such, I have no access to my domain’s DNS records.
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Adding a My_Webapp page and setting it as the default – both as domain.tld/site and at the domain root (domain.tld/), and even with a customised HTML splash page explaining it’s a private server run for a family – made the situation worse. Before, VirusTotal said only Google Safebrowsing thought my domain was a phishing site. Immediately after, I had 2 extra companies think so, and “multiple redirects” was the reason given, as before.
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I submitted a request for review here (Report Incorrect Phishing Warning) as I said in my previous post, but so far there’s been no change.
I second what others have said about customising the SSO login screen. I know it has been mentioned in passing that it is possible using custom style sheets (CSS) and/or Javascript, but I’m sure I’m not the only one who would really appreciate a step-by-step guide on how to actually do this in the context of a Yunohost server. Not everyone is a web developer.