I am experiencing this as well! After 5.55 went live, occasionally (especially during 24-man raids) the background music would not play either during or in-between fights. Random other sounds are not playing as well as mentioned by OP, but I have not verified all they mentioned personally. Here is my information:

Date & Time: 6/6/2021
Frequency: Daily
World name: Gilgamesh
Character name: Ozan Hikayeci
Retainer name: N/A
NPC name: N/A
Monster name: N/A
Class/Level: All
Party or solo: Both
In-game time: N/A
Area and coordinates: Void Ark, Royal City of Rabanastre, Ridonia Lighthouse, Dun Scaith, Orbonne Monastery, etc.
Housing: N/A
Steps:
1.
2.
3.
*Add more steps if necessary

Connection Specs
- Type of internet connection/provider: Wireless, AT&T Brodband
- Modem maker/model number: N/A

■ PS5 Specs

Model Number of the PlayStation®5 You Are Using
- Model Number: 3005719

Model Number of the PlayStation®Vita You Are Using
- Model Number: N/A