Ive never used grease on a carbon post.3 of my bikes have carbon posts with a tiny bit of carbon assembly paste.To be honest Im not even sure the paste is necessary.
It might creak or slip without assembly paste.
Grease might have some unfortunate side effects. Depending on the post/frame finish or any scrapes, scratches or if you've trimmed the post. (Unlikely with anything modern)
The frame might also have a metal shim in it.
Just a wee point there, just so its out there, but if the inner frame is unsealed, will the assembly past bleed into or contaminate the raw carbon ? :?
Could it affect it in the long run ?.