I followed Robin Wood's excellent advice and bought a Gransfors Swedish carving axe and it is lovely and I've learnt a lot about axes from it. It is one of my favorite things. It is a bit heavy though (about 2lb+).
So, I also use a very cheap 700g Lidl's axe, made in China, which I have sharpen into a carving axe. I use it as much as my Gransfor Swedish carving axe. The blade flares up & down, which is what attracted me to it - giving it a cutting blade that it a little longer and more curved than a regular modern hatchet. It is now an excellent carving axe IMHO.
What do I look for in carving axe?
1.
Sharp, very sharp. It might be all you need.
2. Deep carving bevels (thinking about 1" deep). Wille Sundqvist (Sweden) and (hence) Drew Langsner (USA) both recommend this. Either symmetrical or right(/left)-hand biased - Robin Wood has some interesting insights on this.
3. Long cutting face/edge - longer than usual (viking style?). Not essential but it just seems to help.
4. Weight: about 700g/1.5lb-ish (i.e. 600-800g) for general carving use. But there is a lot of scope for personal preference, and its makes some sense to use different size axes for different size jobs/people. 500g-2kg?

. #2 Kent pattern is a popular size for general carving use but bigger & smaller sizes can work well too.
5. A slim blade. Gransfors excels at this. HOWEVER, the quintessential carving axe - the Gransfor Bruks Swedish Carving Axe designed by/with Wille Sundqvist - has quite a thick blade! And it's a
great carving axe, but so is my slim bladed Lidl axe & the Gransfors Wildlife hatchet. English Kent-pattern axes are slim-bladed and well regarded for carving, once sharpened
for carving. 50-100 years ago every house in Britain probably had one or two and few people use axes now, so a good variety of used Kent pattern axes are readily available now.
6. A cool looking, great feeling wooden handle that fits your hand well for power strokes & when choked up near the head. But you can always carve your own

Standard handles can be excellent.
Other highly rated carving axes: Hans Karlsson Sloyd axe designed with Wille Sundqvist (I suspect this is the same as the Hans Karlsson carpenters axe sold by Woodland Craft supplies - but I'd be happy to be corrected on that), Ronnqvist viking-style axe, Svant Djarv's various viking style axes. Their shapes are all variations on the Swedish Carving axe - based on/similar to a 1000 year old Gottland viking axe (skaggox?).