How bad is the damage?
That's a good question, as I'm unqualified to judge. It would appear that the gun was either dropped on its muzzle onto a hard surface or struck with something metallic, resulting in horizontal nicks across its face. At least one such intersects the junction of the crown, and whether this actually creates a raised area in the barrel's path is not clear.
When I asked a local gunsmith about cost he was unwilling to estimate without the gun in his hands. Since I haven't a lot of experience in the cost of re-crowning alone, my question is simply whether it would be more in the neighborhood of tens of dollars or hundreds.
Thanks for your interest.