It’s completely random far as a I can tell and usually when I’m home on Wi-Fi. I’d have the Hub performing perfectly with regards to notifications, automations, recording clips, etc. than out of nowhere I’d have most, if not all, of my HomeKit devices go “No Response”. When they eventually come to, notifications are sent for anything and everything, even with my filters set. After 30 or even more minutes, there would finally be signs of a return to normalcy.
The issue with the auto switching of Hubs is not the fact that it’s switching but that it’s not a seamless switch.
Ona side note, since you mentioned it, the activity zones with my HKSV cameras are working pretty flawlessly.
That sounds like a network issue. Like Bonjour, HAP or some other protocol Apple uses isn't playing nice with your iPhone or accessories or anything. Its not uncommon for the network to work perfectly fine but a function like Bonjour not work giving the appearance the router isn't to blame. Start by power cycling your router and iPhone if you haven't already.
HomeHubs are only used for remote access and aside from AirPlay and Siri control of devices aren't required. When you are home on your local network your iPhone is communicating directly with your accessories. So if you see 'no response' at home the issue is between your iPhone, router and accessories.
The reason I bring up network, specifically your router is because ALL the accessories going on the Fritz is not impossible but unlikely. Your HomeHub switching its rare but it typically happens when the network connection is lost and another device its the opportunity to get in first and be the new connected device (my connected HomeHub has been my office AppleTV since 15.1.1 and before that it was my right HomeHub for a month or so since an electrical outage). Also you are getting a flood of notifications,
The notification thing is odd and while I'm still leaning toward the network the HomeHub could be playing a role in the issue too. After a lot of reading to see how notifications work with HomeKit it would appear the accessory is sending all the notifications to the device that is connected be it iPhone, HomeHub etc and the push notifications are don't want shouldn't be notifying you. The fact you get a flood of them seems like they were all waiting around but its hard to find quality information on that mechanic since Apple is doing most of the leg work.