Well, I'm not an expert on what is regulatory in Europe but here is what I know about the FAA:
https://www.faa.gov/about/office_org...rpretation.pdf
The way I read this FAA interpretation is that so long as there is uninterrupted audio when power is removed from the ANR, then no regulations are being violated even under part 121 (Gulfsteams do not operate under Part 121 as they are not certified to carry more than 19 passengers). Specifically:
"Aircraft equipped with ANR headsets which rely on batteries to provide flight crewmembers with the capability of communicating with air traffic control, crewmembers, or passengers must be capable of providing uninterrupted communications as required in § 121.318 and 121.319. Any failure of the headset to provide this communication capability due to loss of power would be contrary to the provisions of § 25. 1309(a)."
The Bose QC25s do not lose audio when the batteries die so even if I were Part 121, you would not be in violation of 25.1309(a).
As for the G550 and installed equipment. I do not think the aircraft was certified with headsets installed and therefore there is no regulatory requirement to even use headsets.
In the MMEL, 0 headphones are installed and 0 headphones are required so long as hand mic and speakers are operational.
Again, I'm not an expert on European requirements so perhaps a fellow PPrune member can add clarity pointing to specific European regulations requiring the use of TSO headsets.
Cheers!