I ran into this problem and solved it, so this Q&A is here just in case somebody else spent time on sifting through Microsoft's docs trying to find this answer.
How do you create a new board in Azure DevOps? When I go to the boards > board and look at my existing boards, there's no + button to create like there is with repositories in the board list dropdown. Additionally, there's not an add button in the top right. And the board settings are just board preferences, not overall boards management.
As it turns out, in Azure DevOps you can only create boards by creating a team. The team board is created as a side-effect of creating the team. Merely creating a board without the team isn't possible in their paradigm as of this writing.
Sources:
Manage and configure team tools Configure and customize Azure boards