How do I prevent Safari from not saving suggested passwords during password reset flow?

I've just tried to change my Facebook account password. Safari has autofilled my current password, then I've requested to suggest a new password, which was also autofilled into new password and new password confirmation fields. After I clicked the Change password button I've got browser notification, warning me, that if I leave the page, it won't save anything, therefore I've chosen to stay. And that caused the newly suggested password to be not saved into the Key Chain, while it's been changed in Facebook. As a result I have no clue, what my Facebook password is and I have to "reset forgotten password" now.

This issue annoyingly is plaguing Safari on Mac OS, iOS and iPadOS for many years. Experience within the app is even worse, as then the embedded browser window does not even suggest a new password. At least that used to be the case. And since I've got my FB account locked out several times in the past this way I'm only trying to change password via browser now.

The issue affects many other sites as well, where password changing is implemented on pop-up and/or redirects during the process.

I think there are few ways to solve it, but at least storing the suggested password temporarily in the Passwords app/KeyChain would allow to find the suggested password.

[Re-Titled by Moderator]

Original Title: Password reseting flow is broken in Safari for many sites, when trying to use a suggested password as new