In general… weird things happen to Apple devices when the network services they depend on (to quickly communicate between each other on your network) are disabled, out-of-date, or in any kind of corrupt or malformed state (which it almost always is).

You want to sign in to your routers Admin GUI, and look for the following:

1. Something like: “Multicast”, “mDNS”, “Multicast DNS” or equivalent.
   Make sure this is not off or disabled.
   The intended purpose of mDNS is for your router to act as a “zero-configuration” resolver for the hostnames & IP addresses on your network, and its what Apple/AirPlay/AirPrint/AirDrop/HomeKit/etc… use to route their many-to-many device relationships – I.E. every iPhone to any other iPhone/HomePod/TV/etc…
   You may only be able to toggle in on/off, or you may have a select/radio-button option to pick some specific thing. Use your best judgement, or reply here if unsure.
2. Something like: “IGMP Snooping” or equivalent.
   Make sure this is not disabled.
   The intended purpose of IGMP is to have your router monitor your LAN traffic and route mDNS streams & requests directly between registered clients, rather than have those clients chatter back & forth on the entire network.
   Probably on/off, and should not give you multiple options. Reply if unsure.
3. Somehow confirm nothing is reserving or using “.local” for their own routing on your network.
   mDNS uses “.local” exclusively to alias the names of devices on your network that have advertised that they prefer to communicate that way. If you’ve reserved it manually, or some development environment (Valet, MAMP, etc…) has, this is a problem that needs fixing.
4. Make sure all wireless TVs & HomePods have excellent wifi signals. Not just good or acceptable; excellent. For every 1db lost from “full” signal strength, expect 2x data packets to be retried exponentially.
   Give them a clear line-of-sight – no obstructions, walls, plants, chairs, tables, etc… Everything between them will cause attenuation & signal degradation, resulting in dropped data packets & weird behaviors.
5. Restart everything, doing the router last.
   DHCP reservations (IP reassignments) rotate unless they are pinned or assigned manually. Usually, restarting a device will force it to reconcile its network assignments, including IP addresses, hostnames, and mDNS by association.
6. Sometimes (and this is my experience) if you have multiple “home hubs” like you do (TVs, HomePods, etc…) one of them has a tendency to work better than the others. For me, when one specific Apple TV is the “active” HomeKit hub, everything is fine, but any other hub causes all of my automations to never fully finish. I am convinced this is an Apple bug with their own on-device mDNS caches, but haven’t dug into it.