Helping my sister get some networking back to an outbuilding in her back yard.

They have conduit ran underground have have already pulled power through. She wanted to get internet back there aswell. I know 100m is max rated length for CAT6. The actual run would probably be a bit shorter, say 90m and about 80m of that would be running in the same conduit as 240v AC. I plan to just have an AP back there powered by POE+. I’m worried being near the max run while also running right next to AC will not allow a 1Gbps connection back to the outbuilding. Anyone have experience with this?
They could possibly run fiber, but I’ve never messed with it and I’m not entirely sure what hardware I would need. And it would make the outbuilding side much more complicated.

I use unifi equipment.