None of this will work.
What bugs be about Apple is this need to be so rediciliously proprietary that upgrade-ablity concept has been literally thrown out the window. Like you asked...
If so, can a Bluetooth 5.0 replacement for the network card be purchased somewhere?
The answer should be yes. You should be able to get a PCIe WiFi/BT card from a different manufacturer like Dell or HP (or even Apple themselves) and upgrade it for additional features. However, Apple immediately puts a stop to that by tweaking the AirPort card's firmware so that only its drivers will work.
If the 2018 MacBook Pro had continued to use the PCIe slots instead of soldering to the board, you could have theoretically swapped out the AirPort cards from one to the next and still have all the native Apple drivers. Unfortunately, you can't.
Your solutions are limited:
- Get BT 4.0 headset/earbuds specifically for you Mac
- Upgrade your Mac
- Try an external BT dongle (not recommended)
Apple has traditionally not played nicely with more than one BT dongle attached so I would avoid. You can try - it won't break anything (physically) but macOS probably won't appreciate having two BT devices and you could break some functionality.