I think you may have buried the lede:
I put carbon paste on all of my carbon seatposts before installation and every time I pull it for inspection. For this seatpost, like another poster mentioned, I had to go to 6nm as the seatpost slipped at a lower torque setting.
A couple of odd experiences from the past. I rented a mid-range MTB from the really good shop near the entrance of Acadia National Park once, and the seat post just kept slipping and it was clear that others before me had just about trashed the binder QR clamp by maxing out the force they could apply to the QR lever. Turned out there are way too many seat post sizes in the world (hit the diameter filter
here for the laundry list of sizes 0.2mm apart currently for sale, or check out
https://sheldonbrown.com/seatpost-sizes.html for the historic variety). Took it back to the shop to find out they had swapped in a seat post .2mm too small.
Then there is spec variance as shown in this article
https://bike.bikegremlin.com/3114/seat-post-diameter-sizes-standards/ with a Thomson measuring almost 0.2 too small. If a new seat post is looser than an old one, it's probably is best to head to a shop with calipers like those shown to measure both--one might have been pulled from the wrong size bin and mislabeled or be from a defective production run. On the clothing front, I've seen numerous instances of "shrinkflation" where the exact same bike short, jacket, etc. is 1/2 to 1 size or more smaller than it was pre-pandemic. Not saying CC did this, but every measurement comes with a +/- spec. aiming for the low end could save some carbon and resin over lots of components. We see this more in tires where measured width is smaller than spec.
Once had a steel bike with a welded on seat post clamp lug that was where the tabs for the binder bolt were slightly angled--boy do I wish I had paid more attention to that and waited for another frame to come in rather than being so psyched to ride my new bike. That angle put angled tension on the binder bolt, as only the inside edge was tightening the binder, requiring it to be over-torqued to hold, and then the lug cracked. In researching appropriate seat post binder tension after that,
Park Tool lists 4-6.8 nm (so in absence of a spec, you were within industry norms), but one source I found at the time said 3-5.
Finally, hard to tell from a picture, but it looks like the gash in the side of the seat post could be a column failure, which happens when a tube is supporting a high compressive weight, and then it takes far less of a side impact in the middle to collapse the tube than when it is unloaded. That's what happens, for example, when a sailor loses grip on the spinnaker sheet (rope) under load, and the middle of the spinnaker pole bashes into the shroud wire and snaps. It looks like either (a) there was a sideways hit to the saddle (bike fell over hard, a crash, or perhaps you landed on it off center on a big bump?) or (b) the binder area has deformed from a circle crunching in one side, which would happen in clamping down a slotted opening on a too-small seat post. If the binder area deforms, all bets are off. A mechanic somewhere once advised that to keep things nice and round when putting a binder clamp on a slotted opening, put the clamp opening on the front so the two openings don't line up and risk deforming towards a tear drop shape. You might want to put a metal post in there for now and reverse the binder to make sure it is round before the next carbon post goes in.
