I agree that a lot of this is beyond most end users and some of what I am going to mention is not capable with typical consumer routers, or services.
If you have a public IP address that does not change (or changes very seldom), or have a domain name with a Dynamic DNS service, there are free services that will check to see if your internet is alive and report via E-Mail and / or text if it is not. To make it better, if you have internal services that are NAT forwarded so they are reachable from the internet, those specific services can be reported. For example, I have an environmental monitor in my data cabinet that can be reached from the Internet, and my monitoring service can let me know if that device is not responding. One advantage of an external service is that if you loose all power and / or Internet, the service can still send you notification - unlike something running at your house that will have no way to get the message out (even it it has backup power). I am using a service called Uptime Robot for this. They have more involved paid services as well, but what they offer for free meets my needs. They can be found at: https://uptimerobot.com/
As for internal monitoring, the advantage is that an internal device generally has access to things to monitor inside your local LAN that in most cases, something on the Internet can not detect / monitor. However you have to have a device that is capable of testing your devices. In my case, I am NOT using a consumer router. My Mikrotik router can have scripts written that will ping devices on my local LAN and report if something fails to respond. All of the about 60 IoT devices on my various LANs are tested by my router every hour. If any fail to respond, I receive an E-Mail. For an example, a few days ago we had a very short (about half second) power failure (or a really serious dip). Two of my V2 cameras locked up. The next hour I was notified of the failures and a simple power cycle of those two cameras brought them back up. There are both hardware and software solutions for local network monitoring.