HAs that are MFI compatible only works directly with iOS devices and don’t work directly with standard Bluetooth devices.
If the HAs has an intermediate streamer option then this intermediate streamer will work as an interface between the standard Bluetooth device and the HAs.
So if you want to avoid buying an expensive TV adapter to your HAs which works via audio or Toslink optical connection, then you buy a standard Bluetooth adapter like you mentioned, AND the intermediate streamer and both of these can replace the TV Adapter.
The intermediate streamer may be just as expensive as your TV Adapter, but at least it’ll work with any standard Bluetooth device (while your TV Adapter won’t). The trade-off is a clunky intermediate streamer you’ll have to wear around or neck or clip on your shirt or in your pocket.