I personally haven't experimented with Web Bluetooth API a lot, but I think you're looking for Device Discovery and Request Bluetooth Devices:
This version of the Web Bluetooth API specification allows websites, running in the Central role, to connect to remote GATT Servers over a BLE connection. It supports communication among devices that implement Bluetooth 4.0 or later.
When a website requests access to nearby devices using navigator.bluetooth.requestDevice, Google Chrome will prompt user with a device chooser where they can pick one device or simply cancel the request.
The navigator.bluetooth.requestDevice function takes a mandatory Object that defines filters. These filters are used to return only devices that match some advertised Bluetooth GATT services and/or the device name.
Also, here's the list of GATT Services.