I got a 6 month sub going, and I looked at my next billing date, which is 29th of March 2023.
Do I miss out on getting this mount with my current 6 month sub due to the next billing date being next year, even though the mount comes with a 6 month sub?
Players on an existing 6-month recurring subscription with a future renewal date will receive the Nether-Gorged Greatwyrm mount, and Tabard of Flame for Burning Crusade Classic at no additional charge, no later than July 22, 2022 (must be redeemed by December 31. 2022).
Seems to me you’re fine, check back by 22 July.
Mine didn’t appear until today, the news hit before the mounts got sent out. This is usual 
Yes, mine appeared today too. Keep checking the little parcel icon at the top of the app and eventually a small orange dot will appear so you can click through to get the reward.