For me, it is easier than smoking smokeping. But smokeping offers more details by pinging the same host 20 times each run. This can help to discover packet loss.
If you want it REALLY easy, you should be able to write a simple bash script that, when called, pings an arbitrary always online website like google, and if the ping returns an error, sends a telegram message to your phone. you could also store the current state in a separate file to allow for "is now down" and "is up again" differentiation, then use the telegram message timestamps to "track" (loosely used term) up- and downtime. To call the script, add it to your crontab and specify your test interval there.
no, telegram is cloud based. you send the message via a CURL POST to the telegram API, which contains your bot token and message. details are in the linked guide.
Kuma obviously is more established and feature-proof, and will work great for most people who want notifications like this. I just wanted to take the prompt for a "simple alternative" overly serious 😎
Probably the only true way of knowing is by setting up an EXTERNAL host somewhere on a VPS or maybe a reputable VPS provider. Then, on that provider, set up Uptime Kuma, or if you don't want to go through that trouble and don't mind a potential 10 minute gap in knowing, https://uptimerobot.com/ which checks every 5 minutes and sends an alert.
Once you do this, unless you have a Static IP, you will want to register with a DDNS provider so you can then tell the uptime service to ping your DDNS host which should echo back . If your internet is down, it won't echo back and then it will trigger their alert. Of course, this won't work if your IP changes, so staying on top of that is key unless you use a router which auto updates it which a lot do now days.
Or, if you use Cloudflare Tunnels, it can be configured to alert you when the tunnel is down or unhealthy (A.K.A. No internet or the server is rebooted).