With regard to Li-ion battery fires, if they are charged at too high a voltage and consequently begin to overheat there is a risk of catching fire. But what about after they are charged properly and just sitting around. Is there still a risk of something happening? For example, is my rattle gun that has been sitting in the shed for six months untouched something to be concerned about, or should the battery be removed and put in a strong metal box? What about as the battery gets older despite not having done hardly any work?
Power tool batteries from major brands tend to be fairly reliable when properly handled, there are some reports of fires but not too many. The failure can occur during charging, during use, or in storage. If you want to be completely safe then yes you'd store them on a solid metal bench or metal cabinet and have a working smoke detector in the room.
In your case, a shed burning down probably isn't the end of the world though.
https://www.worksafe.govt.nz/about-us/news-and-media/battery-fire-in-underground-storage/