I welded in the brake bridge today, which represents the final welding that needs to be done on the bicycle frame. The bridge seems a little far from the tire, but it looks like it is not so far that calibers only touch the tire rather than the rim. I think this is perfectly adequate for the first frame. Honestly, I just feel grateful to have been able to reach this point.

Does this mean that the brakes will wear the tire and potentially damage it over time compared to the brake pressing entirely on the rim?
Yes, the tires may be gradually worn over time. This is not ideal and I should keep in mind for the next frame to move the bridge a bit closer to the tire. I think though that since the brakes mostly touch the rim I can get away with this problem for a while.