There's a lot of layers here, so let me work backwards from the edge, inward:

1. You lost power, so you probably lost internet if your endpoint hardware was not also on a UPS. Nothing is going to stop that unless you get a multi-WAN router, and an LTE backup on standby. Probably not worth the cost.

2. You shouldn't have lost DNS or DHCP for your local network just because of a reboot. Something is wrong with your setup, and we'd need more info about said setup to say more, but generally these services are stateful for the most part, and shouldn't lose state on reboot IF you have them configured properly for your local domains, like a DNS forwarded, and static reservations on DHCP for local devices.

3. You don't need HA for all your services. You need to fix the issues with your services not running properly with interruptions. The specific services you mentioned don't behave poorly of they die and come back in properly configured environments.

4. If you have a UPS in your home, all devices connected to UPS should be getting information about the status of said UPS and shutdown cleanly when thresholds are met. Install NUT somewhere, and upsmon on all your hosts to properly issue shutdown signals when you lose power, and the UPS starts discharging. The thresholds you set for this are up to you.

In general, you don't need to overthink HA, you need to focus instead on your services recovering gracefully in these situations. Spending insane amounts of time and money to make highly available services for your media and home automation will only leave you having spent resources and realizing there is no way to ever get to 100% uptime without flaws somewhere.