support.discord.com and discord.com login and logout (in)consistency

When you log out (sign out) of support.discord.com you don't get logged out of discord.com -- you can still open and use the Discord web app. When you click "Sign in" on the support site, you get logged in without Discord asking for your password and your two-factor authentication code.
When you log out of discord.com you don't get logged out of support.discord.com. When you click "Login" on discord.com you have to give Discord your login credentials and two-factor authentication code.

Signing in to Discord's support site will sign you in to the Discord web app too. Signing in to the Discord web app won't immediately sign you in to Discord's support site, but clicking "Sign in" on the support site will do without you having type in any login credentials.

So, I think that either:

• support.discord.com and discord.com login and logout should be completely separated:
  logging out of Discord Support would not log you out from Discord and the other way around. Same with login (would not log you in).
• support.discord.com and discord.com login and logout should be completely united, merged:
  logging out of Discord Support would log you out from Discord too and the other way around. Same with login (would log you in).

Either if one of the two will be implemented or not, the Discord login page should tell you at least that signing in to one of the sites will sign you in to the other as well, and signing out of one of the sites won't sign you out from the other.