Hello Alexey,
Good to see you in Microsoft Community.
Firstly, could you let me know the specific system version? You can check it by pressing the Win key + R key, and typing "winver", then press Enter, please take a screenshot/photo of it, and only send the relevant information without PII in the next reply.
You may Run the audio troubleshooter. Select Start > Settings > System > Sound > Troubleshoot common sound problems and select Output devices or Input devices*.*
You mentioned that you deleted the connected Bluetooth device and connect it again, did you do it in Windows Settings? I recommend that you uninstall the device in Device Manager, then restart the system and connect again. "Win*" + "X" > "Device Manager" > "Audio inputs and outputs", find the device, then right click > "Uninstall device"*, then reboot.
Meanwhile, I recommend that you confirm in the sound settings that the device has been set as the default audio device after connecting your Bluetooth headphones. Win + R to open*****"Run"*, type "mmsys.cpl" and press Enter to open the "Sound" interface, right-click your target device in the "Playback" tab and "Recording" tab respectively > "Set as Default Device", then click "Ok" to save the settings.
And you may Perform a clean boot to check if the headset is recognized correctly, this is a troubleshooting step. In this mode, we can further confirm whether it is caused by system problem or third-party software or personalized settings. So, please be patient.
Disclaimer*: A “clean boot” starts Windows with a minimal set of drivers and startup programs. It helps to determine whether a background program is interfering with your game or program and to isolate the cause of a problem.*
These steps of "clean boot" might look complicated at first glance. However, to avoid any trouble for you, please follow them in order and step-by-step so that it will help you get you back on track.
If anything is unclear, please do not hesitate to let me know.
Best Regards,
Mosken_L - MSFT | Microsoft Community Support Specialist