The problem is in its natural form

That option has nothing to do with the LightDM login screen that you go to when restating or when you force a full log out of your account. The only thing it does is control if you need to type a password or not to get in to the computer after it puts itself to sleep. in other words, it is for the lock screen and not for logging out the whole user account.

This is thus a non issue and working by design. Along with that, any Budgie issues should be reported here on the Budgie bug tracker and not on the Solus Development Portal.

In T8630#163925, @Jacalz wrote:

That option has nothing to do with the LightDM login screen that you go to when restating or when you force a full log out of your account. The only thing it does is control if you need to type a password or not to get in to the computer after it puts itself to sleep. in other words, it is for the lock screen and not for logging out the whole user account.

If this is true, then it loses its essence. It’s strange. This option in Solus 3 allows you to automatically log in to your account without entering a password.

Sorry I don't think it ever did, but I might be wrong.

So how can you disable the need of inputing password after reboot? I used to do that , but then I still had to input password when launching an app that uses Gnome Keyring to unlock it, Vivaldi for example

I think that more or less is in the LightDM settings. Try installing lightdm-settings and using that to change some setting there, I think it might work (was a long time since I used it)...