100LL aviation fuel, is actually only about 96 octane, if you measure it with the automotive fuel octane method, R+M/2.
No, 96 octane gasoline will not do harm to a gasoline engine. Though the lead in 100LL could cause issues with catalytic converter(s).
Many aircraft which were actually built to run on 80 octane, have been running 100LL for decades.
Too low an octane, can cause detonation, (knocking). Too high an octane, only results in money being wasted.
The octane an engine needs is basically determined by the compression ratio. Although, with electronics engine makers have been able to push those limits.