Which flooring is suitable for underfloor heating in a music room in the basement?

Music room? Thick heavy touchfloor carpet. Carpet on the walls too. If not immediately acoustic foam.

"They will be heating themselves stupid and senseless"

The good lady is poorly educated, misinformed, or simply can't do the math. Parquet floors (multilayer/click etc.) are an absolute standard in new buildings with heat pumps and underfloor heating. Of course, tiles are more efficient, but whether I have €44 (as in our KFW55 new building from 2021 with almost everywhere parquet, even in a basement room) or €54 monthly heating costs is totally irrelevant. One reason for tiles in the basement would be, from my point of view, better sealing against water (washing machine, flood, rain, etc.) and the fact that you don't have to worry about the dew point in the humid midsummer.

Also carpet on the walls. If not, then acoustic foam right away.

Of course, not without additional measures on exterior walls ;)

What does music room mean, flute, bass guitar, drums or even a whole band as a rehearsal room. Think of a visual indicator for the doorbell, so people outside don’t wait forever, and acoustic decoupling of the living floor