The Ozone Layer is considerably lower than the Ionosphere proper, and protects all surface life from ionizing solar UV radiation. It most likely is as damaged by rocket exhaust as the ionosphere, and much more slowly healed.

That undoubtedly deserves its own article, which will unavoidably be confused with this one and be considered old news.

Why would O3 be damaged by H2O? SpaceX rockets are powered by hydrogen and oxygen and produce water as exhaust.

Kerosene and oxygen.. Anyway it's probably that the exhaust plume will contain reactive species like nitrogen oxides, maybe the water vapour could have a role. It's not a big effect.

Hydrazine powered rockets have a much bigger effect (all those nitrogen oxides) and are still not a very big deal.