I am in no way an expert, as evidenced by my recent thread on this topic, but I have done a ridiculous amount of reading on this the last couple of days and my understanding is that the Network decides which is the home hub, so you’re fine.
The HomePod shows as active because it doesn’t turn off (it’s waiting for a command - the only way to turn off a HomePod is to unplug it), but the TVs are on standby because they’re off until you turn them on. It doesn’t mean they’re not networked, communicating to each other and ready to do whatever you ask.