java.lang.NullPointerException
	at yeelp.distinctdamagedescriptions.integration.crafttweaker.types.CoTDDDDamageTypeBuilder.register(CoTDDDDamageTypeBuilder.java:65)

This suggests that the damage types registry isn't initialized yet. Didn't come up in testing, which is odd, but is probably just due to mod load order and I got (un)lucky in testing.

Save the damage types to be registered in post init or something, similar to the distribution builder.

Actually that doesn't work. They need to be initialized in pre-init in the DDDCoTIntegration's pre init callback. Before that, the registry might not be initialized. After that, config tries to load and the damage type must exist by then.