Yes, Reaper does have a scan log. I created a shortcut on my desktop to it.
On Windows, the file is located at, and called:
C:\Users\Primary\AppData\Roaming\REAPER\reaper-vstplugins64.ini
[Replace "Primary" with your username]
I set Windoze to default to opening Notepad for .INI files. Here's a small section:
SPAN.vst3=00EC7AEBB08CD201,555746558,SPAN (Voxengo)
SPL_Attacker.vst3=B63B055F1358D301,1872302934,SPL Attacker (Plugin Alliance)
SPL_Free_Ranger.vst3=00269A8E374AD301,2074663543,SPL Free Ranger (Plugin Alliance)
Tape_Multi_Track.vst3=00B127C6C35ED301
Tape.vst3=0084F6C4C35ED301,1563913648,Tape (Softube)
Tempo_Delay.vst3=00BA5C11E618D201,1791662028,Tempo Delay (Voxengo)
Notice that the "Tape_Multi_Track.vst3" line is incomplete, compared to the rest. That tells you that it didn't scan properly (makes sense, in this case; it's a Studio One MixEngineFX).