I thought maybe with application of some more coats it would smooth out, but that doesn't seem to be happening.
If you were French polishing it could if you took it far enough (i.e. spent enough time on it!) but very broadly speaking grain was filled before application of shellac started, and this would have greatly lessened what you're seeing here I think.
What would be the best way to smooth out the surface?
You have a few options. The first is to sand back a little or a lot right now, then continue applying shellac.
The second is to begin applying shellac again, until it basically smothers the grain irregularities. It's hard to tell how much would be enough without at least a little sanding, but you would normally be abrading slightly at some point in the process and it can be now, later (at a certain stage during the buildup of coats) or basically right at the end when you are perfecting the surface.
Personally I'd have no hesitation in sanding this back now then applying more shellac. Not least because it will give results you can see immediately, which is reassuring, rather than having your fingers crossed that later on a certain amount will do what you want, with the ever-present risk of sanding through somewhere along the arrises and especially at the corners.
Here, by sanding back I mean sanding until all or virtually all of the texture is gone; which will mean exposing bare wood. You want to back the abrasive with a hard block to help keep the surface as flat as possible as you sand.
Just for future reference:
I sanded the surface to 320 before applying shellac
This is unnecessary when applying a film finish. Because a film finish literally builds a film on the wood — the surface of the finish becoming the final surface — you can generally stop at around 180 grit, and sanding further yields no benefit. And in some situations you can actually stop sanding at 150 without sanding texture being evident after finish application, and without the final result looking visibly duller or anything like that.