After extensive testing, I have gathered a full list of disparities between the old biomes_client.json and the new client_biome system.

1. Several 'client_biome' biome identifiers are missing from vanilla biomes_client.json
Here's the complete list

birch_forest_hills_mutated
birch_forest_mutated
deep_dark
desert_mutated
dripstone_caves
frozen_peaks
grove
jagged_peaks
jungle_edge_mutated
legacy_frozen_ocean
lush_caves
meadow
mesa_plateau_mutated
mesa_plateau_stone_mutated
redwood_taiga_hills_mutated
redwood_taiga_mutated
roofed_forest_mutated
savanna_plateau_mutated
snowy_slopes
stony_peaks
pale_garden

These are valid vanilla biome identifiers that are never referenced by the vanilla biomes_client.json, and only exist as client_biome files in the more recent client_biome system.

Note:
It seems appropriate to include these biome identifiers and their water and fog settings in the vanilla biomes_client.json file, assuming it is not going to be deprecated ( ? )

2. Several 'biomes_client' biome identifiers are invalid when used in new 'client_biome's 

Here's a complete list of the identifiers that exist within the vanilla biomes_client file, but are absent from the vanilla client_biome files, and when attempting to create these client_biomes manually, the biome IDs are marked as invalid by the game.

mega_spruce_taiga
mega_spruce_taiga_mutated
mega_taiga_mutated
mesa_mutated
and possibly:
default

Notes:
Since apparently the new biomes_client does not function anymore, it is expected for the new system to have a Default biome client that will be used as the default biome configuration, and for the new client_biome system to cover all previous existing biomes.

It could also be the case that some of these biomes (aside from default) are simply obsolete and are unsued leftovers in the old biomes_client even in latest Minecraft resource versions found at: aka.ms/resourcepacktemplate

I am unable to verify this and a word from the developers would be greatly appreciated.