>I think, that the extra sharpness might be because of lost detail

It may be because of high output impedance as well. But maybe yeah, it's a distortion.

I personally found Xiaomi phones to be problematic with software sound chains by default (effects, equalizers that you can't turn off, problems with gain, etc). So maybe DAC/Amp in your Redmi are not that bad, you just need custom firmware like Pixel Experience or something like that to keep software sound chain clean.