EE overrides vanilla dragon nest and makes it 1 block higher. EE tweaks vanilla code to make the egg spawn 1 block higher, but your codee does not and 2+ eggs dont spawn.
Solution: change the code to

World world = event.getEntity().getEntityWorld();
BlockPos pos = world.getHeight(Heightmap.Type.MOTION_BLOCKING, EndPodiumFeature.END_PODIUM_LOCATION);
while (world.getBlockState(pos).getBlock() != Blocks.AIR) pos.up();
world.setBlockState(pos, Blocks.DRAGON_EGG.getDefaultState());

nest 4 blocks height instead of vanilla 3

BlockPos pos = world.getHeight(Heightmap.Type.MOTION_BLOCKING, EndPodiumFeature.END_PODIUM_LOCATION);

This gets the topmost empty position at that location. I don't think moving the block higher would help?

BlockPos pos = world.getHeight(Heightmap.Type.MOTION_BLOCKING, EndPodiumFeature.END_PODIUM_LOCATION);

This gets the topmost empty position at that location. I don't think moving the block higher would help?

It gets the topmost position for vanilla generation. EE replaces bedrock blocks with its own (and it does it very strange, because, for example, when you delete DIM1 folder and let The End generate second time, it generates without the nest (?!?)).
And Ive just built this code and tested with EE, it works.

Hmm it might only see full blocks.

• no working in 1.19.2

BlockPos pos = world.getHeight(Heightmap.Type.MOTION_BLOCKING, EndPodiumFeature.END_PODIUM_LOCATION);
This gets the topmost empty position at that location. I don't think moving the block higher would help?

It gets the topmost position for vanilla generation. EE replaces bedrock blocks with its own (and it does it very strange, because, for example, when you delete DIM1 folder and let The End generate second time, it generates without the nest (?!?)). And Ive just built this code and tested with EE, it works.

give please 1.19.2 Forge worked build