Arduino relay shields are abundant, along with real-time clocks, and now, built-in WiFi. The tough part will be coming up with apps and web interfacing, but that's not totally necessary either.

Arduino has launched its next generation of UNO boards, introducing a 32-bit Renesas microcontroller and Espressif ESP32-S3 module, one-click cloud connectivity and plenty of I/O plus a 12×8 red LED ...

Again, it might sound obvious, but any gadget you’re connecting to a WiFi network has to actively seek that connection. This will only happen when its WiFi mode is on.

Now for the minutiae: there’s an Arduino Uno with built-in Wi-Fi that receives UDP commands from a phone to raise and lower the clock at the appropriate times.