I tried to purchase this frame on Aliexpress back in November. After I already paid for it, the TanTan rep sent me an email saying it was out of stock and issued a refund after we had a short back and forth over other models that were available. They did say, at the time, that they would be available this month. Not sure that helps, but I'd reach out to whichever TanTan rep is currently working on Aliexpress to doublecheck availability before purchasing.
As for TanTan and spare parts, yeah, i'm not sure how many years from now you're anticipating having to get a spare part, but I purchased my TanTan frame back in November and as recently as a week ago, Lisa who I bought the frame from, is still answering emails and sending parts as requested. I had a random screw fall out which she replaced free of charge and I also purchased a spare rear deraileur hangar. I've asked about other parts they might have on hand and have had 0 issues getting answers.
I can't speak for the TT-X3 or BB386 specifically, but as far as TanTan frame quality goes, I've had 0 issues with the pressfit bottom bracket on my frame. It's a BB86 and I've recently switched out the Shimano 24mm BB86 threaded pressfit for a 29mm DUB pressfit. Alignment and tolerances are excellent, both installs were super easy, and no creaking from either.