Without Fabric API, the game doesn't launch, and just opens an "Incompatible mod set!" popup (even though no other mods are installed). The popup itself also doesn't adequately describe the missing dependency, instead claiming that the wrong versions of Fabric Command API and Fabric Item API are present inside Fabrication itself. Fabric API isn't listed anywhere on CurseForge as a dependency either, and the wording on the top of the Github issue submission page ("only Fabrication, no other mods") implies that the mod would work without it. So, I'm not entirely sure whether the issue here is that Fabrication doesn't say that it depends on Fabric API, or if it's not supposed to depend on it at all (hence the weird issue title). Adding Fabric API allows the game to launch with no issues.

latest.log file

The launcher also generates a stacktrace, but it's identical to the one at the bottom of the log file.