Silly question, but do you reckon it'll function decently in a Kotlin multiplatform codebase? There's swift native code, but I'm not sure how it would perform with some logic being shared.

Not silly at all. For Compose Multiplatform, Axiom won't do much for code review or generation. It might be useful for operations on the built app: console capture, crash symbolication, simulator UI/accessibility driving, CPU profiling, plus the whole shipping layer (signing, privacy manifests, submission).