How do I seal the bottom plate along my foundation?
The framing should have been installed with foam known as sill seal. If it wasn't, you could use any caulk such as silicone to seal against air and insect intrusion.

I'm a bit confused why I see drywall directly against masonry like that. Normally you have energy walls built inside the foundation, and the framing laps past on to the upper wall, such that the entire wall is adequately insulated and a vapor barrier is applied. The combination of all these things usually results in a completely sealed wall.