Welcome, Sofie.
You can likely get by with most anything you elect to do on such small applications, I would think. But if you've got that massive edge to work with, and apparently weight is not a concern, I think I'd elect to use both the plywood, for compatible structure with the wood edging, and the CBU for a more compatible bonding surface for the tile. Seems we're entering the realm of structural trivets, eh?
Likely stick the CBU to the plywood with a construction adhesive. I'd use 1/4" Hardiebacker because of the ability to make cleaner cut edges. I suppose you could just rabbet the CBU into that Walnut edging and eliminate the plywood if you're so inclined, but the plywood, glued to the edging, would make it a good bit stronger.
I'd want to grout the tile installation with a cementitious grout. That will likely crack around the perimeter eventually, but I think I'd prefer that to taking a chance with a flexible sealant under potentially hot pots.
No real rules to follow for your particular project.
My opinion; worth price charged.