Pine plywood (project panel) looks quite different than pine boards (select)
This is quite normal, and unfortunately unavoidable, even with much higher quality plywood like Baltic-birch ply if the goal were to match it to some some solid birch. Partly is it simply because wood can vary (and sometimes a lot).
But also the ply's surface is a veneer — and these days almost invariably a radially cut slice taken from the edge of a spinning log by a gigantic knife, not a slice through a log (which would look like the surface of a board). So even when there is a good colour match, as there can be sometimes, the grain/figure is so very different the plywood screams "I'm different!" And as if that's not enough the slicing process means that the surface of plywood accepts most stains very differently to the same/similar solid wood.
I plan to stain everything fairly dark, like an espresso color. Will I have a hard time getting the finished product to look uniform on all faces, given how much darker/yellower the plywood looks?
You're lucky as only going quite dark like this will easily allow the two materials to look more similar. But, it matters greatly what you're staining with.
If you go with a conventional staining product, a liquid product that sinks into the product to colour it, then you'd have a much harder time than if you use something like "gel stain".
So-called "gel stain" is actually a coloured varnish that has been artificially thickened, and is so well suited to pine (a notoriously blotch-prone wood that is hard to stain evenly) that one finishing guru has quipped that it might as well be called "pine stain".
I also found a 1/4" sheet of birch project panel that looks almost identical to the pine boards in its natural shade. I'm wondering if that would be a better choice
It actually could be, if for no other reason that softwood plywood can be of such low quality. It's often only suited to rough work, or at best shop cabinetry (where appearance is of secondary importance to functionality).