So, what if the Core group of skills had Basic Crafting as it is (but that would include basic cooking in furnace) and some sort of Basic Machine Crafting (allowing building all machines apart from Forge as well as craft all basic recipes in them: so, no separate skill to build a machine and separate to craft things).
Then in Crafting group there would be Advanced Machine Crafting (opening advanced recipes in machines unlocked previously and allowing to build Forge and craft everything in it; also unlocking furnace recipes like glass and cooking buff foods, so all the persisting and floating etc.) and Bulk/Mass Crafting (self-explanatory).
Last step is the specialisation or unique crafting skills in separate skill group being unlocked a bit further down the path. Wouldn’t open any new machines or recipes, just give skills allowing creating items with bonuses (in case of items with stats, such as tools and weapons) or additional patterns and colours and looks (in case of decorative building blocks, clothing, furniture etc. or maybe even items creating buffs like healing etc. that can be placed inside beacons to give builds actual function). Examples: Hammer Forger, Slingbow Crafter, Forge Master (better chance of successful upgrading tools, a few unique upgrades not available from Advanced Machine Crafting?), Interior Designer (extra props and decor) etc. Also including Power Coils Crafting here.
So, unlocking crafting would happen in 3 steps:
Core Skills: 2 skills (Basic Crafting and Basic Machine Crafting) covered in Tutorial and covering not just Workbench and furnace as it is now, but also basic recipes from all machines (apart from Forge) and basic cooking in Furnace for starting characters.
Crafting Skills: 3 skills (Advanced Machine Crafting and Bulk/Mass Crafting) covering Forge and unlocking advanced recipes in all machines that weren’t covered plus allowing Bulk and Mass Crafting.
Crafting Mastery: several skills (Power Coil Crafting plus all imaginable unique bonuses/recipes unlocking skills) - cost of those skills should be such that no character could unlock them all. To be true, ideally one character would only really be able to cover Power Coils (obvious choice) and 1-2 specialisations (like Hammer or Slingbow or Furniture or Cooking special skills) - imagining that there would be no more than 10 -ish skills like that. This way crafters become unique characters offering unique items of just few types and those looking for such items wont be able to get them from just one crafter.
Crafting the way we know would be covered in 2 easy steps with 5 skills - Tutorial asks for rather symbolic price in skill-points and advanced part would have moderate cost, so affordable for even none-crafting character builds. It’s only the last group that would make a character a real crafter as opposite to hunter, miner, builder, explorer or generalist (skill point cost would have to be really high there).