Post#1 was not missed by everyone but it took some time to work through potential problems in the data and research information for responses.
Kernel v5.12 is no longer supported on Manjaro and is no longer available from Manjaro repositories
I suggest you install latest supported kernel v5.14 using Manjaro Settings Manager GUI (manjaro-settings-manager -m msm_kernel ) and uninstall kernel v5.12
OR use these terminal commands
sudo mhwd-kernel -i linux514
sudo mhwd-kernel -r linux512
HP website for this laptop is showing latest BIOS firmware version F.67 Rev.A released on 27 Aug 2021. You should consider updating BIOS firmware.
Instructions for the Sony headset suggest they may not be suitable for use with a laptop
MDR-ZX310AP Operating Instructions
Compatible products
Use this unit with smartphones.
Notes
* If you connect to an unsupported smartphone, the microphone of this unit may not function, or the volume level may be low.
* This unit is not guaranteed to operate digital music players
The instructions also explain how the remote control button on the headset cable can control Android
phones and iPhones.
I suspect that the headset jack is using a CTIA wiring standard, but the jack socket on the laptop is likely using OMTP wiring standard
Phone connector (audio) - TRRS standards | Wikipedia
The diagram in this post shows the different audio connections used by the two different jack wiring standards
It might be possible to get the headset to work with an audio adapter to change the audio connections, but the remote control button on the headset cable might be capable of muting or reducing the microphone volume even if all the audio connections are correct
See this blog post that explains there is an Apple CTIA standard that includes additional remote control signalling from their headsets that is not compatible with the AHJ/CTIA wiring standard on other Brands of mobile phone
Audio levels might also be changing because there are 2 incompatible sound servers running
Sound Server-3: PulseAudio v: 15.0 running: yes
Sound Server-4: PipeWire v: 0.3.38 running: yes
See this post for how to either disable PipeWire services or replace PulseAudio