Hi Joseph,
I cannot provide any recommendations or answer your question about which option will remain. Unfortunately, I do not have that information, and I really wish I knew more (you can refer to this thread here for why Juno uses internetcomputer(dot)org).
Regarding the “unusual behavior” you noticed, let me try to explain. When you create a new anchor with Internet Identity, it becomes valid for sign-in purposes for the specific domain on which you created it.
For instance, if you create an anchor on identity.ic0.app, you will only be able to use it to sign in on that domain. If you try to sign in on a third-party dapp like Dscvr, that dapp should request you to sign in with identity.ic0.app specifically to use the anchor you created. If it asks you to sign in with identity.internetcomputer.org, it won’t work.
The same applies in reverse.
When a developer implements the AuthClient of agent-js, they can define which II domain to use. However, commonly and by default, identity.ic0.app is still mostly used.
It is possible to set an anchor to be valid on multiple domains. For example, my personal anchor works on both, allowing me to sign in everywhere regardless of the II domain used. Nevertheless, I understand that the UX for setting up such “cross-domain” functionality in II is not yet optimal and is not well-documented.
I hope this answers your question, at least regarding the why and what. Let me know if anything is still unclear.