I wonder, is it a possibility for me to copy the settings of a Softsynth that I've put in one project into another? In other words, is it possible for me to copy a softsynth from one project's synth rack into another? If so, how would I do this?

Not directly but...

- in source project, open VST window
- save VST preset using dropown (say onto desktop)
- open target project
- insert VST
- load saved VST preset

KPerry
Not directly but...

- in source project, open VST window
- save VST preset using dropown (say onto desktop)
- open target project
- insert VST
- load saved VST preset

What's Dropown?

That's supposed to be "dropdown" - the menu that drops down when you click on an arrow at toward the side of a field. 
 
You might find this tip of the week useful in understanding what you can do with the VST header.

I routinely save presets under the name of the song I used them in. That makes it easier to recall, when I remember them in the context of how they were used previously. 

And if you have a complex setup, such as a bunch of loaded instruments in Kontakt, or drum cell output routings for Battery, you can create a Track Template, and that will also save your audio and midi tracks that you select, in addition to whatever buses and synths you include.
 
I do this all the time.
 
Bob Bone
 

bitflipper
I routinely save presets under the name of the song I used them in. That makes it easier to recall, when I remember them in the context of how they were used previously.

 
I usually save plugin settings for a given project within the project folder itself, in a sub-folder called "Settings", rather than storing them within the plugin's own folder structure. This way they are easy to find when you need them and they don't get deleted or overwritten when you update or reinstall the software.

I recommend saving the track as a track template. Then, in another project, you can insert a track from that template, and all the settings from the original track will be in the new track.

I LOVE track templates - with a small number of clicks, I can load up a track template that brings in a bunch of complex bus, audio, and midi tracks and settings.
 
Bob Bone