REAPER only runs its plugins in stereo-in stereo-out configuration. Like many algorithmic reverbs, BlackHole does not keep the channels in the stereo path completely separate. Generally, this is a desirable thing because in a reverberant space, reflections aren't isolated left and right.
For your specific use case, since you want to get discrete left and right reverb signals, I would recommend running two instances and changing the I/O pins so that the first instance has input and output on channel 1 only, and the second instance has input and output on channel 2 only. Screenshots below.
For the right channel plugin's configuration you could alternatively send 2 to Input L and Output L to 2, though I prefer the configuration below.