Your commitments, your accounts and the deals you are chasing — beside the company plan, without sharing a database with it. Access belongs to the board, so what an invited collaborator sees is a decision somebody made, not a flag somebody forgot.
Use the email your invitation was sent to.
The account picker is limited to @halopowered.com, but that is a hint rather than a lock. Access comes from an invitation either way — which is also why an invited collaborator on their own domain can use this button.