The way gnome-keyring works is that normally when you don't have autologin enabled a default keyring automatically gets created and your user login password is is used to unlock that default keyring. Now because you have autologin enabled, the keyring doesn't know what password to use to unlock the keyring where the credentials for Skype is stored. You can configure that keyring the unlocked without password, but the credentials for Skype still automatically get saved in the keyring.
I tried all of this myself to verify it, now here's the thing the Skype because seems to have a dependency on "gnome-keyring". So it seems to Skype is packages to automatically store you Skype credentials in gnome-keyring so that's the reason why that is happening. I tried another application, discord. When I login to Discord reboot and then open Discord again I found that Discord also automatically logs the user in but there are no credentials saved in they keyring, I found that in the users homedir $HOME/.config/discord.
However I'm getting the idea that this is the normal behavior of modern chat apps, I also found
a post on reddit about a Discord user who is on Windows who was also wanting for Discord not to remember their password.
To verify this I installed an old(and opensource) chat app called "Pidgin" together with the plugin for Pidgin,"purple-discord. I was able to login into Discord on the Pidgin chat app. I then rebooted, opened pidgin again and this time Pidgin was asking for a password to login to Discord. Pidgin does have an option to save your password.
I also did some searching and it seems with the Windows Skype client there are
a few ways around it, not the easiest ways either for a non-technical person. I also came across this post.
So this person is having the same issues as you but is use KDE Plasma and only having issues with Skype, while the other programs they are using are doing as they want, not remember there password.
Also decided to install KDE Plasma on my Debian vm to test out both Skype and Discord. KDE Plasma uses sddm as Desktop Display Manager and also
supports auto-login. As I already assumed the Skype packages still depends on gnome-keyring so automatically logins after you login the first time into Skype and Discord reacts the same way as well as I had tested with Cinnamon.
After having tested out an old chat client, a new chat client, another Desktop Environment(on Debian) and having read those posts it still seems to to me that modern chat apps are designed that way. So whether you are using autologin or not modern chat apps seem to have a way builtin whether into the app or by using os authentication tools to have your credentials saved so that you only have to login once and after that they automatically login when you open them.
So in short it differs per application what is used to store the credentials of the user but it seems most modern chat apps are designed that way. Although I think that would be modern proprietary chat apps and the only exception I have come across so far is the Linux Microsoft Teams app, I don't know what opensource chat apps would do since I don't use any like that are similar to Discord and Skype. I would think you would have more options with those since opensource apps tend to give you more choice in what you want. So there's no solution an opensource os(Debian or any other distribution) can give) for a choice that a proprietary app makes. I know it's not a solution you were hoping for but it's at least an answer, which I hope will give you at some satisfaction of understanding why it's not working as you want.
So I don't know what other programs you are using that you are having the same with where the login gets saved even after a reboot of your system?