Should I install the full 32GB of RAM if my CPU supports it?

Yes. If your CPU officially supports 32GB, that’s the maximum it can handle — and installing exactly that amount is perfectly fine. The “supported” number is the ceiling, not a suggestion to stop short. Just make sure the RAM sticks are on your motherboard’s QVL and you’re using the correct slots for dual-channel configuration. Don’t try to install 64GB on a CPU that tops out at 32GB — that won’t work.