I am logged into Trello and can view a private board.
I have embedded this private board in a Confluence Cloud page, using the included Trello Board macro.
Instead of displaying the Trello board, the Confluence page shows “Board not found. This board may be private. You may be able to view it by logging in.” As mentioned above, this browser is already logged into Trello.
If I click the “logging in” link in the embedded Trello view, a new browser window opens, then quickly closes again (presumably because I'm already logged in).