I don't see how a streamer could possibly alter the harmonics or tonality/tonal balance of an audio system. It is only the apps loaded into streamers that could possibly affect one of these two parameters of sound quality, music players such as Roon, Qobuz, Tidal, etc. and DSP engines. To claim otherwise is arguing that digital packets of 0 and 1's have inherent tonality/ timbre. I also don't see how any music player app or dsp engine can change timbre, timbre/harmonics live solely in the analog realm. On the other hand I do agree the apps and dsp engines could change the tonal balance.
Streamers sole impacts are in resolution, transparency and presentation, this why minimizing noise and providing highest quality clocking is so important. When people are claiming their streamer adds some character to the sound they are conflating the contributions of other parts of their audio system with the streamer. A high quality streamer simply allows the 'color' of the rest of the system to shine through. The color, harmonic texture comes solely from the analog components of system, the only digital component that can alter this is the analog output stage in a dac. No network or digital data processing component has a 'sound.'