In Pcbnew, my +3V3 net is connected to the filled zone on the B.Cu layer. In the picture below, you can see that Pad 5 is properly connected to the filled zone, but Pad 2 is not. However, you can also see that Pad 2 is on the same +3V3 net as Pad 5.
What must I do to convince Pcbnew that I want the filled zone to connect to Pad 2?
Also, I can see from the thin rounded rectangle around your +3V3 pads that you have the plane’s clearance much larger than the net clearance. Unless you have a specific reason for that, you should be able to tighten up the plane (and thermal) clearances down a bit to potentially provide more connection surface for thermals to sprout from. Pin 5 should get one more and pin 2 might get one more.