I lied, it doesn't work, sorry for the spam.
So if somebody (a real person) could help, it would be really appreciated.
Ok, Thanks to ChatGPT (yeah its real), i've found a solution.
After discussing with him about the ps8moduly.cz 's code, and after he tell me that i should do it with override(i know), he tell me that the main reason for this error should be "Session Initialization : the session might not be fully initialized or updated during the very first visit to a new cart. This could potentially affect the behavior of the code".
So i asked him how to repair that.
He tell me to add this below code before the ps8moduly.cz 's code :
// Make sure the session is started and initialized
if (session_status() !== PHP_SESSION_ACTIVE) {
session_start();
}
And it work. (I'm still testing every checkout process, but i've seen no problem for now.)
So thanks to ChatGPT and @ps8moduly.cz, this thread is [SOLVED], thanks !