It is not difficult to carve bowls and dishes with hand tools. Some would say tedious.
There are a bunch of different methods with regional popularity.

1. Scandinavia: Dough bowls and kuksa usually start with a specialized hand axe or an adze.
The puzzle is control and accuracy to make a row of strikes. Granfors make some, Look for a Swedish blade smith: Hans Karlsson. Next, all the fine work is done with crooked knives such as the Mora (Sweden) #162, #163 and #164.

2. Pacific North west coastal region where I live. Green wood, usually alder but birch and western red cedar and yellow cedar are OK. The shaping is done with an elbow adze and it is fast. The best bladesmiths to look at online are Kestrel Tools and North Bay Forge and Cariboo Blades. Crescent Knife Works in Vancouver markets blades through Lee Valley. You can see them online as "Haida Carver's Knife Blades." I have 4 of those. You have to be prepared to haft the blades and learn how to take a blade with a progressive sweep and keep that carving sharp.
Fine work is done with crooked knives. You're far better off to buy the blade(s) and haft them yourself. I have 12 crooked knives. Scratch-built handles and hafted 10 of those.

3. For spoons and dishes, I commonly make a stop cut with a 12mm - 15mm Forstner bit in the middle of the dish void. I carve back down into that with a 9/15 & 30oz lead core mallet. All the finish work is done with crooked knives. With 50+ spoons finished for sale, yes tedious.

4. To get started, find a store that sells horse-shoeing farrier's supplies. Buy a pair of Mora #171 Equus Hook knives and change the bevel from the factory 30 degrees to 12 degrees. The handles are OK as-is = I'm still carving with the first pair I ever bought, maybe 10 years ago. The bonus is the little scorp-like hook at the tim and with a single bevel, you can push them around. (Lots of crooked knives are double bevel.) I know of 14 different brands of Farrier's Hook Knives. We can buy just 3 of those here. They are really tough steel, meant for the rough work of trimming horse hooves. Tuned up, pretty dang good in wood, too.

Hope these things give you some ideas.