I think what you see on a client is just the status of tuners that are accessible on the client. It is not the status of tuners on the server.
Since HDHomeRun tuners are network tuners, they can be accessed from any computer. The fact that your cable tuners (HDHR Prime) are not seen on the client probably just says you did not install it on the client. Your new device is a bda device, which does not require installation on your part, because Windows will find the appropriate drivers and install them for you.
So, your client computer can access the new 4K tuners and MC treats them as if they are local tuners. When you play a channel, MC first tries to load a local tuner. If it does not find a local tuner, it goes to the server. Since the tuners are actually not local, but are network tuners, there is a chance of conflict - the server and the tuner trying to use the same tuner simultaneously - which would lead to bad behavior. It is best if you disable the tuners on the client and let the server handle all network tuners. If you want to keep the tuners available on the client (as local tuners), at least you should order the tuners on the client differently from the order on the server. For example, you can order the tuners as tuner1, tuner2, tuner3, tuner4 and order them on the client as tuner4, tuner3, tuner2, tuner1, to reduce the chance of conflicts.