The AI gets more reinforcements, as well, and it takes a higher AIP before reinforcement amounts stop scaling with AIP. Also, there is a point where if there are enough defending ships in a system, additional reinforcements will be freed as threat; the thresholds for that are lower for higher difficulties.
You get less warning for waves/CPAs/etc at higher difficulties.
At difficulty 8+, if a CPA launches and there's an exogalactic strike force at least 60% charged, it'll launch the exo early to hit alongside the CPA. Also on 8+, the AI can also choose to delay launching waves to try to synchronize them with a CPA.
Higher difficulties tend to have more 'brutal pick' core guard posts on the AI homeworlds. I think they may also get more AI Eyes, ion cannons, etc.
I think there may also be some tuning parameters in the AI logic that are difficulty based, like how long it waits before doing certain things.