The bug
With the new world-edit, if you enable any experiments, it will disable the achievements in that world. The old world-edit screen does not do this. This should also be the case for the new world-edit screen.

Steps to reproduce

1. Create a new world with the new world-edit screen enabled
2. Enable any experiment, for example Holiday Creator Features
3. Create the new world
4. Check the in-game settings whether it says Achievements cannot be earned in this world.:
   

Expected results
The player can still earn achievements after enabling experiments using the new world-edit screen (like the Holiday Creator Features)

Observed results
The player no longer can earn achievements after enabling experiments using the new world-edit screen.
The player can still enable achievements if the old world-edit screen is used (as workaround)

Extra information
Using a NBT program it is confirmed that if you enable the new world-edit screen, any experiment will turn of achievements, under the setting in the level.dat called hasBeenLoadedInCreative where the value is set to 1 (true)
If any world is created with experiment in the old world-edit screen, this value stays at 0 (false) for any experiment enabled in the world
The images are from 1.20.10.24 Preview, but have also been confirmed in 1.20.20.21 Preview

Media
The images provided show that the hasBeenLoadedInCreative setting has been set to 1 for the new world-edit screen, while it remains at 0 with the old world-edit screen

1. hasBeenLoadedInCreative is set to 1 with the new world-edit screen (The world is called 'Achievements OFF new UI, but that is not important)
   
2. hasBeenLoadedInCreative is set to 0 with the old world-edit screen (The world is called 'Achievements OFF old UI, but that is not important)
   
3. The experiments that are enabled for both the new and old world-edit screen