We will likely be doing the same thing a few months from now, so please follow up if you find some useful information. I've done a lot of SSO, but not yet with Sharepoint, so I don't yet have anything specific to share, but:
"After 3 days searching the web without finding the answer (understandable for me !)"
Did you find some things that looked like they may be very useful to someone with a different background? You may have found a perfect explanation which would make sense to me, for example, which I could use to make a module you could use. Feel free to post any URLs and ask ask "what does this mean?" (also feel free to email/msg me, as I might not see a reply here.)
What I can share based on implementing SSO systems before, and based on my background in cybersecurity, is that if you care about the system being at all secure, beware of any writing any custom code, especially for the core SSO handoff. The bad guys know what the common mistakes are, so it's very, very easy to get that "wrong". For example, I can identify two or three vulnerabilties in code I've never seen just by looking at the filename. (Example - any script called"download.php" virtually always includes the same three errors.)
If you decide that you do NOT care about security because in your case it doesn't matter if someone acesses an account, just be sure to clearly mark that in several places so that your successor doesn't place high value data under the protection of your insecurity system.