I love birch plywood but I don't think it will look very good with an oak face frame. The two woods will stain to a different shade and the grain will contrast no matter how dark you make it.
Poplar, aspen, or mahogany would be better choices for the face frame. Birch would also work, obviously, if you found some.
I would also make the bottom lip of the face frame a bit more than 2" so it acts as a more effective substrate dam.
I'm not sure how moist the dirt substrate will be in your cage. It can't be that moist for a Uromastyx, though, so I think a plastic laminate of some sort on the floor and an oil-based polyurethane on the rest of the cage should be sufficient.
If I understand your other question, I would go ahead and stain and polyurethane the entire cage, floor and all. Well I guess you won't need the stain on the floor.
Then put down the plastic laminate on the floor, then use a polyurethane caulk along the junction of the plastic floor and cage walls. It won't match the color but your substrate will be deep enough to cover it, I assume.
The only stains I would avoid are the ones that come premixed with polyurethane. These won't work well with birch, IMO.
Here is a picture of my GF's bearded dragon cage. Birch plywood with a mahogany stain. Look over on the side where the basking light is. The glowing red look is really what the cage looks like.
I'd go this dark or darker for the exterior and lighter than this for the interior.
You might also notice that I don't have a face frame on this cage. Instead I have two strips of 6" wide birch plywood stretching between the two sides. Cheaper than a face frame and no worries about matching. Also hides the lights nicely.
If you go back to the picture of the oak cage you'll see I did the same thing. But with that cage I added some inexpensive molding and corner rosettes to give a finished look.
This provides a more open look to the cage if you're using sliding doors. The moulding on the oak cage also hides the glass edges a bit. A look a like and allows you to cut your glass track short which allows for easier cleaning.
