Configuration:
Minecraft: 1.19.2
Fabric loader 0.14.9
Cloth config v8 (8.0.75)
Fabric API 0.60.0+1.19.2
Transite 1.0.0

All the tools (and sword) seem to effectively harvest no matter what the tool(s) are currently targeting as the "form" (e.g. a Transite Sword saying its a "Transite Hoe" is still able to effectively mine ores, obsidian and gather snowballs).
Example:
https://user-images.githubusercontent.com/22578581/185346749-2e31d8b0-54f8-4d12-8edc-9aafa7a68427.mp4