Plugin Manager in Reaper?

Another way to see ALL your VSTs is to go to View/Assets/FX Browser (or View/FX Browser).
 
If anything is missing, just open preferences, and go to Plug-ins, then choose VST.  You will see a listing showing the path(s) to all your VSTs.  You can then add a path to any VSTs that are missing and then hit Re-scan.
 
Obviously it's preferred to have all your VSTs in one convenient location, but certain products insist on installing to proprietary locations.
 
One other thing - Reaper can read both 32bit and 64bit VST, so (presuming you are using a 64 bit version of Reaper) don't bother installing any 32bit VST if given both 32bit and 64bit options when installing a VST.   If you ONLY have a 32bit VST for a certain program, then Reaper can use it without any additional bridge type programs.  However, I suggest you create separate directories for 32bit and 64bit VST files so that if you have other DAWs, you can use those VSTs in their 32bit and 64bit directories without problems.
 

Kev999

discoDSP
It looks like Reaper doesn't have a scan log...

Shame. I expected it to be a standard DAW feature.

Reaper developers do not do things just because they are "standard", especially if the standard is not logical, has general design inconsistency or can be confusing.
In respect to this problem: VST is just a DLL file and there is no "hints" that DLL is VST. To detect VST, Reaper (or other daw) tries to "load" it and check that it responds "as a VST". The result (and so the information for potential  log) is:
* the DLL is a VST. Then Reaper will show it to you as FX/Synth.
* the DLL could be loaded, but it does not respond as a VST. That it is not a VST... But itself, that is not an error, VST folders can have other DLLs (f.e. DLLs used by some VST)
* the DLL could not be loaded. If that is really VST, that is the only case when you may want to know the reason. But there can be non VST, as in previous case, which can not be loaded and that is ok. Also the report will be "failed to find xkrjehjrk.dll" (some external dependence), which can be more confusing then helpful for an average musician (and an average programmer will use some external tool like Dependency Walker to get more details).
 
Sorry, back to the topic.
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* Write down "VST Scan Paths" in Sonar preferences and check you have all these paths in Reaper. Note that even "standard" Sonar has several locations for VSTs. I am almost sure you will see all you see in Sonar after that.
If what is not detected are some Waves plug-ins (rare but I have seen such reports), there is a method to fix that. Waves use so called "shell" method (expose one "plug-in", which then gives access to other), the subject of endless discussions in all DAWs.
 
* DimensionPro (at least VST incarnations) and  Philharmonic (the first, so 32bit, and the second) can work in Reaper.
a) check in Sonar which DimPro you have. There was very old DX and more modern VSTs. Reaper support DX, but since you have SPLAT, you also have DimPro as VST 64bit. And that you want to use in Reaper to avoid troubles.
 
b) if you have old Philharmonic, 32bit, it should work out of the box. In fact better then in Splat. I remember I have tweaked something during initial installation, to make it run with Sonar at all. It can be without that it is unable to work in Reaper as well. If required, I can try to find details.
 
c) if you use modern IK products (Philharmonic 2, ST3, Syntronik), VST3 incarnations had problems with Reaper some time ago. So check that you have the latest Reaper version or use VST2 versions of these plug-ins.
 
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Finally, in case you have not noticed the sticky in Reaper forum... You can install my extension to open Sonar projects in Reaper. That can be seen as a test you have all plug-ins used in particular projects
(but first copy that projects somewhere, including audio, and open the copy. I do not want you hunting me later, when you modify the project in Reaper and then Sonar no longer find deleted WAVs...).