My press fit bottom bracket is making an incredibly irritating clicking noise (carbon frame if that’s relevant). What tools do I need to get to fix this?

Ideally I’d like to pop the bearings out, put some grease on them and put them back in again, but I don’t know if that’s possible.

BB86 has the bearings in plastic cups that fit in the frame. If they’re creaking it’s probably the cups creaking in the frame rather than the bearings.

So, you need to get the cups out (headset removal tool or screwdriver if you’re careful), clean and then you’ve a choice – grease, threadlock or ptfe tape to make sure it’s a secure fit.