I would actually use the older domain icp0.app.
Long story short, when I started Juno, we discussed with the community whether we should use identity.internetcomputer.org or identity.ic0.app as the main login domain for II because everything indicated a future migration of the domain. For instance, see “icp0.app flagged by anti-spam” or “follow up icp0.io”. In the first blog post, there was also even, at that time, a mention of the explanation of the migration to internetcomputer.org as described by @sea-snake, which was later edited, if I remember correctly.
Consequently, we opted for internetcomputer.org to spare new users the possible hassle of a migration. However, it appears that this migration has not occurred, and despite multiple requests, I never received an official statement from the foundation about their vision for this particular question. So, right now, I tend to actually think nothing will happen soon, and the vast majority of dapps and users will continue to use ic0.app.