Bluetooth earphone connecting issue

I have a problem when trying to connect my Huawei AM61(also known as Honor Sport AM61 or Huawei Sport AM61) with my Mac (MacBook Air 2017, macOS HighSierra 10.13.6). When I hit the button Connect with my earphones in Bluetooth Settings AM61 device status become Connected and the voice assistant in headphones informs about successful connection. But after about 10 seconds it automatically disconnects. I turned on music in this 10-second time period. The sound was playing by Internal Speakers. In Sound settings no new device appeared. The problem remains with turning off Wi-Fi. Also I have the same issue with others earphones, for ex. Mi True Wireless EBs Basic S. By the way these earphones work perfectly fine with my Iphone 5s.