Issue description:
Searching for sword (or any other tinkers tool) in the creative menu does not show the respective tinker's tool

If crashed, link to crash report (use a site such as pastebin):
N/A

Versions:

• Minecraft: 1.16.5
• Forge: 36.0.42
• Mantle: 1.6.79
• Tinkers Construct: 3.0.2.78

Confirm below that this issue is not covered on the roadmap or "Whats New?"

Can it be reproduced with just Tinkers Construct? If not, list the other mods required to reproduce the issue.
Tinker's only

In recent versions tools were given a way to initialize their data and now they show in in the search tab. Tool parts never will due to how Mojang indexes the search tab.

Duplicate of #4301.

No, different issue. For more context, creative inventory loads on game start. Material list load on world load. JEI also loads on world load, by calling getSubItems as expected, which is why it works except in the case of #4301. I want to leave this open to remind me to argue with the search tab some time. Our dedicated tabs should work

Right, my bad. It was reported already, though, I think.

Looks like fixing this involves messing with the search tree for vanilla, a complex datastructure that I dont' feel confortable messing with. Its either too hard or impossible for me to want to put in the effort.