The best way to do thaumaturgy, imo, would be to take notes from Ventures in Essence and actually go through the entire, multi-step process and/or ritual in order to achieve the thaumaturgical effect or product.
Take the repeatedly mentioned blacksmith and their historical mystical position and prowess. I see no reason why you couldn't do a Craft Venture to blacksmith something, and then introduce obstacles and advantages that leverage occult knowledge, skill, and resources in order to blacksmith something, but with magic. Mechanically it wouldn't be all that different, but the trappings, the feel, the flavor of the overall process, would achieve an outcome I at least would find satisfactory for representing non-Sorcery magic.
THis is kind of my feeling. A lot of what was thaumaturgy in 2e could just be the Ability in 3e. And some of the things that were like, mechancial widget things are just how you do the venture. Talking to spirits, some prayer to a god or another, using special materials. That's just Craft with things different from how we would do it to implement.
Thaumatrugy in 3e's sense is not that. It's more often like, overtly magic stuff not all blacksmiths can do. And I think that's the rub for a lot of folks is that they want a lot of the things that should just be the way you Craft be some mechancial widget you futz wtih. Extend that to a bunch of the other stuff 2e thaumaturgy mission-creeper into.
To me thaumaturgy was trying to cover three things:
Shit that the Abiltiy could do anyways, just made a widget to enable it weirdly. Like using the right ingredients, doing salt line wards right, or the entire Animal Husbandry Art and a lot of the low end Alchemys tuff.
Stuff that the Abiltiy can do, but probalby not everyone who uses the Ability should be able to do. Wards, distilling magical materials from base elements, summoning a demon based on its weird occult habits. These are things that probably are beyond the basic rules, but should be something you could learn to do. These honestly are I think the liminal area where I think that there's a palce for folks to be able to do these...but also for a lot of folks to be able to think or make people think they're doing them but not. Again I refer to the materail from Flat Earth, but you had a few instances of prophets, savants, and even sorcerers who thought they knew what they were doing but didn't. Or characters like Reigan in
Mob Psycho 100 who are honestly cool characters, but who are still mostly normals who know about the supernaturla but can't like, acutally do it.
The final is things that are honestly most misc. supernatural Merit tricks. Things like starting fire due to having a weird abiltiy to cause sparks, genuine abiltiy to see the future, or having some god on tap due to your bloodline. I'm not sure these needed to be thaumaturgy myself. These honestly are more like low-end supernatural beings. And there's a blurry line on what goes into this and what goes into the previous category. Exorcism is an example.
An example of this is to loop again to blacksmithing. Making steel is probably the first category. And they might use means that we consider supernatural ritual to do this, but that's fine by me. That isn't something I would charge folks to use thaumaturgy for, it's a tool used for a venture-style way to crafft weapons.
Making a weapon that needs to be sharpened, can hit immaterial spirits, or which scares off fairies is something I am sure folks claim they have done, but
whether they actually did is something that is context-based. Some people probably can do this. Some peole think they could, but turns out they were wrong. ANd some folks sell these things to foreigners who they know aren't coming back and wil probably die if htey tried anyhow.
The issue is whether the latter is more common than the former. I tend to like it so that it's possible (again better than Earth), enough folks might buy it, but not so common that it's expected everywhere. And whether it's something you could teach people or is it something you have for those legendary swordsmen or bloodlines of blacksmiths people don't trust who seem to make magical swords that never need sharpening? Or could it be both? Dunno. But I think there again, should be room for it to be less-than-assumedt-to-be-always.