Last night (August 18, 2020), I was able to navigate between different boards within the same project.
This morning (August 19, 2020), selecting a new board refreshes the page, but stays at the same board, even though the board selector says that it is showing the new board. Navigating to a new project shows one of the boards in that project, but then selecting a new board in that project changes the navigation, but the board shown is the same.
I have not updated anything on my machine, and do not allow auto-updates, so my OS and Safari installation have not changed.
When I downloaded Chrome and tried it there, it is able to change boards correctly. However, I will not use Chrome as a normal browser, so this is not a long term solution.