You won't find traits in the online editor. I'm using a hex file editor, HxD (any will do, this was the first one I found).
Editing like that might feel intimidating at first, but it's still somewhat easy - BotN saves are a jumbled mix of strings and hex values.
Each creature, including the breeder, is roughly 27KB in size, or a little less than 7k in offset (the values in the left column). Data begins with the character's name, and ends with stats and traits. The order of the creatures is the same as in the game, so if you want to edit the breeder, just search for the first monster's name and scroll up slightly.
Traits are listed as strings in a container,
GameplayTagContainer. They consist of the string length in a hex byte increased by one, three zeroes, the string itself, and an ending zero.
The selected trait is 21 characters long, and counting the zero that marks the end of a string, it gives 22, which translates to 16 in hex (1*16 + 6).
Order of traits doesn't matter, but it's the safest to insert them between other traits.
After you are done modifying the traits, you need to change the container count as well - in the middle of that long dotted line, there'll be a number corresponding to how many traits the creature has. Don't forget to change that as well, or it may break the save, ignore some of the traits, or crash the game on load.
Warning, some of the traits don't have immediate impact on the character, or have additional tinkering involved with them.
For example, biggus dickus will work as intended, but adding the boobage trait will have no effect whatsoever. But since you have the trait, you can then breed that monster, and the offspring generated with it will have them working properly. I think stat-changing traits don't work immediately as well. Additionally, the gaudy trait involves a gaudy tag somewhere in the middle of the creature's data. I didn't catch enough fancy monstrosities to figure out how it works
yet.
Should I post a list of the traits I found?