I can see this checkbox after logging in, and it's missing when I stay at anonymous

If I understand things correctly, I believe T390751 (which @taavi tagged this task as a duplicate of) is for the function being broken on the API side, while my ticket here is the option missing from the form only when not logged in. Both seem like separate issues that affect the same work process.

I must add that the auth.wikimedia.org site does not automatically log in users from existing sessions from other main Wikimedia wikis, which led me to believe that the option was gone entirely.

In T391324#10724747, @LuciferianThomas wrote:

If I understand things correctly, I believe T390751 (which @taavi tagged this task as a duplicate of) is for the function being broken on the API side

More specifically it's about the function being broken on the API side while using a "normal" domain like en.wikipedia.org. Those domains don't generally allow you to do signup (rather they redirect you to auth.wikimedia.org) but the API is supposed to retain B/C and that didn't fully work.

while my ticket here is the option missing from the form only when not logged in.

I don't think there ever was an option for account creation via email when not logged in. The whole workflow exists for the purpose of a trusted user being able to circumvent some anti-spam restrictions. It's just that before SUL3 you wouldn't unexpectedly find yourself logged out on the signup page, and now that can happen since it's a different domain.

I must add that the auth.wikimedia.org site does not automatically log in users from existing sessions from other main Wikimedia wikis, which led me to believe that the option was gone entirely.

Yeah it's supposed to go in the opposite direction (other wikis log you in based on your auth.wikimedia.org session). That works well for normal signup - the reason you land on the signup page in the first place is that you are not logged in on the main wiki and thus the signup link is shown, so little point in trying to obtain a session from elsewhere. Wanting to use the signup page while logged in is an edge case where that behavior ends up being confusing.

As I said, I don't really see what can be done here. If the user arrived via a software-generated link, we could change that link to indicate that we expect the user to be logged in, and they could be redirected to login when they aren't. But there is no such link, AFAIK.

Per @Tgr's comments, the problem here is not a missing option (it is there), but the fact that you won't see this option if your login on the central domain expired, and it's easy to miss this. I will therefore close this as a duplicate of T393459: Warn users when they get redirected from a logged-in local page to a logged-out auth.wikimedia.org page.