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Does your PC have a combined TRRS headphone/microphone socket? Older PCs may have separate sockets for headphones and microphone.
The fact that your headset was supplied with a cable with a TRS plug suggests that the headset jack (socket) only provides an analog connection to the earpieces not the microphone. You could try a TRRS-TRRS cable but I'd be surprised if it worked.
To use the Bluetooth microphone with a PC you could get a Bluetooth USB adapter. Make sure you get one that is specified to work with stereo headphones and a microphone, not one that just works with e.g. a keyboard. More specifically you can check the headset and adapter share common Bluetooth profiles. Devices using the aptX profile should give better audio quality but this isn't supported by all devices. Windows may not let you tell if aptX is in use
Bluetooth versions prior to 5.0 can't provide high quality stereo output at the same time as microphone input over bluetooth (see the previous link). Bluetooth 5.0 devices should overcome this. Alternatively you may be able to use a cable for wired stereo output whilst using bluetooth for microphone input. You'll need to tell your PC which devices to use. For Windows use the sound app in control panel.
It seems that improvements to Windows Bluetooth support are currently (2021-04) being tried out in the Dev(elopment) Channel and should, if successful, make their way into production versions of Windows later.