Left clicking with the chunk purchasing tool does nothing, unless I'm missing something? And when I click from the map view, I get a "cannot unclaim chunk" error message.

It should be tied to whatever controls you have for building and mining, left click / build should claim and right click / mine should unclaim.
Do you have any other mods on? I've never encountered anything like that.

No, I turned off all other mods. It also makes the Undo sound effect, and the yellow lines on the map view also flicker. It's as if it's unclaiming the chunk the very next frame after claiming it.

I'm also playing on version 2.0.59 if that matters.

That does sound like what it's doing, claiming then unclaiming.
There were a couple minor changes to custom keybinds in some recent-ish updates, but I don't think linked game controls have changed at all.
The only thing I can think of is if your build and mine keybinds overlap in some way, which I severely doubt is the case.
I assume there's a reason you're not on the latest stable/experimental version, but I can imagine that might be the cause as well.

I got it to work by changing build from left-click to middle-click and mine from right-click to left-click.
It also works if I just swap the build and mine left/right click keybinds.

Huh, weird. Well, I'm glad you got something working.