Please update the biome api to include the overworld and 3D biomes as it is lacking them and way to force world noise maps to use density functions to override datapacks and mod biome sources

I do not believe density functions are involved in the biome selection. That said, that is exactly why there is no such API: too complicated.

I recommend using other, third-party API mods like Terrablender. They don't provide the same support we do (i.e. does not update to every snapshot) but has more functionality than we can provide here.

As you're probably aware, that is not a biome definition.

What yes they are in noise settings for world gen
https://www.planetminecraft.com/data-pack/better-cave-gen/

That pack is my own and and example

{
"sea_level": 63,
"disable_mob_generation": false,
"aquifers_enabled": true,
"ore_veins_enabled": true,
"legacy_random_source": false,
"default_block": {
"Name": "minecraft:stone"
},
"default_fluid": {
"Name": "minecraft:water",
"Properties": {
"level": "0"
}
},
"noise": {
"min_y": -64,
"height": 384,
"size_horizontal": 1,
"size_vertical": 2
},
"noise_router": {
"barrier": 0,
"fluid_level_floodedness": 0,
"fluid_level_spread": 0,
"lava": 0,
"temperature": 0,
"vegetation": 0,
"continents": 0,
"erosion": 0,
"depth": "minecraft:end/sloped_cheese",
"ridges": 0,
"initial_density_without_jaggedness": 0,
"final_density": {
"type": "minecraft:interpolated",
"argument": "minecraft:overworld/base_3d_noise"
},
"vein_toggle": 0,
"vein_ridged": 0,
"vein_gap": 0
},
"spawn_target": [],
"surface_rule": {
"type": "minecraft:sequence",
"sequence": []
}
}

Depth is for the height dependent noise I picked a random one so it may not be 3d