The dexcom G6 transmitter has only two BT “slots”: 1=(Dexcom_receiver, pump, or something else) 2=(mobile / phone). So in order to bond/authenticate to the transmitter for a BT reading, you need an available slot. Your case sounds like you are already using both slots, so probably not going to get far without changes.
If you were willing to give up the receiver, you could use some code in an ESP32 such as: https://github.com/TheEpicBigBoss/Dexcom-ESP32-Reader in ESPHome which can relay the data to your HA. But, the much easier route is to just setup Nightscout and use the HA-integration: Nightscout - Home Assistant
I have considered hacking together an ESP32 reader so I do not need to have my phone with me while at home, for example. But an Xdrip±WearOS watch acting as a collector from the transmitter is probably a better solution and is already coded, you just need an appropriate watch and phone.
Good luck!