The are dozens of F4 flight controllers out there. Some say nothing about Bluetooth and WIFI and some say one , the other or both.
I want to fly with my trusty Spektrum DX8 transmitter and a DSMX receiver. I am guessing those would work with just about all controllers and that mentioning BT and WIFI just means you can also fly using those with a phone.
Your understanding is partially correct.
You won't have any problem running Spektrum provided the flight controller has the correct voltage output.
You can't use a phone to fly however. The BT is used for smartphone app configuration. The WIFI is a newer addition that will work with the ELRS receiver tech that is becoming very popular.