I've recently moved my old 1.19.4 world to 1.20.1 then I killed the Ender dragon third time to get a new gateway. But unfortunately after the kill the new gateway didn't spawn. But my second gateway seems weird. Seems like game re-spawned the existing gateway. I've also checked that the gateway transfers you to the same old location in the end.

steps I followed

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• open existing 1.19.4 world with 1.20.1 launcher

• go to end and place 4 end crystals to spawn ender dragon

• kill the ender dragon