Periodically checking the sensor graphs on the Home Assistant web interface, or even on the mobile app, is not that great a way to be notified that the pilot light has gone out. It's more of an after-the-fact thing.. I started thinking about more appropriate mechanisms.
I wanted something that I could leave in some fairly visible location, something that could give an indication that would catch someone's attention, and something that would be meaningful to other family members. I considered a lot of possibilities, but I happened to come across these M5 Atom Matrix devices from M5:
These are pretty amazing for a device that costs less than US$10. It's size is 24 x 24 x 14 mm (approximately 1in x 1in x 1/2 in) and houses a 5x5 RGB LED matrix. Inside is an ESP32. It's powered through a USB-C connector and exposes connectors for several GPIO pins. There is a reset button on one side. The top face (with the LEDs looking out) is actually an enormous button that you can read through a GPIO. And, of course, it's got the usual wifi and other goodies you expect from an ESP32 device.
Once I started looking at this device, I stopped thinking I could make something better. Sure, it might be way overkill for the job I am giving it, but did I mention it costs under 10 bucks? Others had already worked out how to use it with ESPhome (for example, https://github.com/rnauber/ESPHomeMatrixLED), so I felt pretty confident about getting it to work. All that was left for me was to figure out how it should listen for status updates and what it should display for each possible state.