Yes, backwards compatibility is expected. But some combinations probably won’t work.
Bluetooth is more hardware and firmware than software; hardware and firmware usually part of the wireless networking and Wi-Fi networking chip.
Your external app or device or whatever would present whatever Bluetooth standard it presents, and the two ends negotiate.
Newer Bluetooth chips and newer Bluetooth versions are intended to be backward compatible with older devices.
Bluetooth 2.0 is from ~2004 or so.
You mention “trying to work with”, and targeted the question for other third-party app developers working with Apple platforms. Please elaborate a little on the issue or limit or problems here, and on the general goals. Are you working on an app? Trying to get some old audio device working? Something needing EDR?
Here is the usual path to Bluetooth devices: https://developer.apple.com/bluetooth/
Apple does not have particularly good Bluetooth diagnostics or troubleshooting tools for recent macOS versions, unfortunately. And the old Bluetooth Explorer tool hasn’t been updated and has been removed. And ~none are accessible in iPhone and iPad.