Absolutely, yes: workspace safety is crucial and even before they try to add the forge (in a safer location than right next to the woodwork!) a fire cabinet makes sense in a shop thats got woodworking going on.

Is jumping straight to a fine on their first fire inspection before they’ve even set up the forge warranted? How exactly did the fire inspector end up showing up now?

I’m probably rooting for small-business-owner-gabi too much, but it seemed like a bit of overkill for a first inspection - especially when this universe apparently doesn’t require a lumber mill to provide helmets for workers.