I have a right angle inside edge that I want to bevel. However, when I try and use the bevel tool it just slides straight down the z-axis and does not actually create a bevel there.
OK so I just tinkered and figured this out on my own. I wanted to leave this here in case anyone comes across this same issue.
The problem is that I had multiple edges in the same place. This was a result of the Spin tool I had used to extrude the handle of the mug.
The solution was to select each edge and choose Mesh>Clean Up>Merge By Distance, set to the minimum, and 'Unselected' enabled:
And now it works as expected: