Papaver somniferum needs more space than that if you want big flowers. I’ve never grown them in a pot but in the ground a good plant would fill nearly a square foot. They grow two to three feet tall. But they don't transplant easily because of their tap root.

IME, breadseed or other annual poppies are best with direct sowing. They are very sensitive to root disturbance or damage to their taproot.

I grow PAPAVER RHOEAS from seed every year and transplant it a couple of times. Most make it without too much fuss. The brutal spring wind does much more to set them back than any amount of transplanting. If it is still cool where you are, I would gently knock out the entire potting mix as one clump and then tease out as many bunches of 2/3 plants as possible without damaging too many roots. If it is a well draining potting mix they should separate easily w- use your finger tips to, start at the bottom of the clump or the sides and gently shake to separate. Keep out of the sun wind and cool for a few days after transplanting. Myine are now in bud and starting to bloom.