Reading through https://www.mass.gov/doc/toxicology-of-the-lithium-ion-batte..., especially seeing the skin impact of a battery combustion in someone's pocket, is enough to make me think I should keep an inventory of every Li-ion battery in the house.

Rechargeable lithium batteries pose a higher risk than single-use lithium batteries. Only the rechargeable ones have a thermal runaway hazard. I figured it was wise to get rid of old rechargeable lithium batteries that I no longer need or use.

Fwiw, there is a BurnBuster brand of fire extinguisher for stopping lithium runaway. See ASIN B0DZ9R7Q51. It is a ripoff but probably good to have.

Single use ones too can contain fluorine, but not the runaway risk. Nevertheless, they require significant care to avoid shorting during storage. Never store them loose or where they can contact each other. Tape them well from all sides, and put them in a sealed ziploc bag before disposing.