What HillRider says. I run Sora 3503 shifters with FD-5504 in the front and Deore RD-M591 in the back and Deore M590 (48-36-22) crankset.
You can run the new ST-R3030 in this case. You may or may not need to change the front derailleur to the "road" one. Also, you may have problems with brakes if you have "long pull" ones.
Another problem is a significant elongation of the effective reach: trekking bars shorten the reach compared to the flat bars, and drop bars extend it compared to the flat bars.