Yongnuo has three distinct trigger systems that are mostly incompatible:
- The manual system only 560 / 60x [YN-560-TX, YN-560IV]
- 622 TTL / HSS compatible system [YN-622-TX, YN-685]
- The Canon RT system (cloned) [YN-E3-RT, YN-968EX-RT]
As you have discovered, these three systems are not directly compatible with each other. But the 622 system can be put into "603" mode and used in the 560 trigger system. But the RT speed can not. In most cases, you only want to use gear in one system.
There is a completely different system where you can control both a $ 65 manual flash with a $ 110 TTL / HSS flash, and the Godox X (2.4 GHz). A Godox XPro can control both a TT600 and a TT685, and you will have HSS and remote power control with both flashes, and TTL with the TT685, as well as expansion options including larger lights and compatibility with other brands of cameras.
See also: What are naming conventions for Yongnuo flashes?