Are thermobaric weapons considered a conventional weapon under international law?

See title question. As far as I can tell from my reading, a key mechanism of thermobaric lethality seems to involve its chemical compounds. For example:

If the fuel deflagrates but does not detonate, victims will be severely burned and will probably also inhale the burning fuel. Since the most common FAE fuels, ethylene oxide and propylene oxide, are highly toxic, undetonated FAE should prove as lethal to personnel caught within the cloud as with most chemical agents. (Wikipedia)

And

Imagine taking a deep breath then submerging yourself in water. Then imagine having all of the oxygen forced instantaneously from your body. Try to inhale again. But instead of cold water filling your lungs, toxic, flammable particles start killing you from the inside out… (Independent.co.uk)

While the explosion itself is perhaps comparable to a conventional explosive, it seems that the chemical lethality is a non-trivial component. Wouldn’t this classify it as a chemical weapon?

Lastly, and maybe this alludes to the answer:

the only reason thermobarics aren’t a war crime in fact is because the international community has yet to officially name them as cruel weapons (Forbes, 4 years old)

Any insight would be great.