It's pretty deep, that's for sure; and anything that fits it isn't going to break out
! I would assume that this is most likely a .50 bore with a 1" octagonal barrel? And that you are not going to be shooting in excess of 150gr charges and 500gr bullets? You are almost certainly fine, it's not THAT deep. As always, when you cut into a barrel, I recommend reproofing it... outside of the stock. I do 1.5x charge and the heaviest projectile I will shoot, seated approx. 1" off the powder. Mark the barrel every 1/2"-1" down the barrel, take good measurements with a caliper, fire the proof load 3 times, measure and compare the dimensions. So long as there has not been a dimensional change in excess of .002 (and no observable changes... like, say, bulges, cracks, or you can see rifling through the side of the barrel
), I would say you are fine. You could un-breach it and pound a slug down the bore before and after, but honestly, I feel that's overkill. These are modern (read: consistent) steel barrels, made from solid stock that has been gun-drilled and heat treated... if it were a fine skelp shotgun barrel from the 1850's, I would be a little more concerned.
I would carefully clean up that dovetail bottom, though, more for appearances than anything. A new sight can be found, or you can make them, they aren't that difficult (especially ones that simple).
This is why I like to solder things on, not because I can't cut dovetails, but everyone makes an Oopsie every now and again (and most of the barrels I work with don't have much margin for oopsies). But dovetails don't need to be that deep, just enough that if you grabbed the item dovetailed in, and tried lifting the rifle with it, it wouldn't pull out.
Best of luck