So, this is caused by a driver problem.
- The first time that I added the TOZO T6 on my PC, it was detected as a hands-free device, and I didn't offer an option to change it to the stereo one.
- The next time that I paired it, it was connected as a stereo headset and didn't output any audio anymore, leading me to this post.
So I tested a number of Bluetooth configurations, and at last, I played with the devices on Device Manager. There's an order to get the hands-free functioning.
- First, you add the T6 normally.
- After that, you go to the device manager and disable both TOZO T6 devices.
- Then, you go to the Bluetooth devices, disconnect the T6, wait a few seconds and turn off the Bluetooth.
- At this point, your T6 will be turned off or disconnected. Certify that they are indeed turned off and turn them on again, they will inform "pairing"
- Turn on the Bluetooth in the Windows, and now your T6 will be paired as a hands-free device. The sound is crappy, but at least is usable.
Well I'll be, this worked. Thanks @Theles