It's kinda outside of COH's expectations. They were flirting with 2K when the shutdown happened.
I have a 29" Ultrawide display (2560 x 1080). Granted, I'm not in 4K territory, but a lot of distortion for sure. For the most part, using Windowed Fullscreen mode and adjusting the Window Scale under User Interface in the Windows Tab of Options helps. Also, in Windows 10, when right-clicking the program you use for City of Heroes (Homecoming, Reborn, etc. depending on your game executable in the I24/25 client folder), click Properties, the Compatibility tab, and give the options under "Change High DPI Settings" a spin. You might get it to look more acceptable with Application as the High DPI Scaling override.
(This advice is client-neutral, it would help with Homecoming, Reborn, coxg, or even Paragon Chat if you need it.)