Hello,
I don’t know if all UR interfaces are similar regarding headphones output but I can share my experience: I own the UR-RT4 and have the same 250 Ohm BD than you. I use them normally with a headphone amp that was designed for 300 Ohm headphones. But I have tested the dt770 with the output of the UR-RT4 and they can get loud. If you ask me, I would never use them at the maximum level that the UR can, because I feel it is loud enough to be unpleasant but of course the maximum level is a lot lower than the case using 30 or 80 Ohm headphones. With the UR I use normally 38 Ohm Audio Technica and to reach the same volume I must just set a fraction of the output level.
Regarding interfaces, I don’t know which one is really designed for 250 Ohm or similar. I doubt that there is one in the consumer grade ones.