I'd go for an ESP8266/ESP32 with a telegram bot and LED (based sign) hanging off it. Just send a msg on telegram to turn it on/off.
That having been said loads of ways to trigger the sign status - it could poll a website to see what status it should display and you have a mechanism of updating that status yadda yadda yadda.
Note that those little chips needs wifi so you'd need to be able to connect it to wifi and have it get public internet access (or whatever you decide to control it). Loads of posts/youtube exist about driving WS2812 LEDs, or making your own DIY LED 'neon' signs. Cool little projects.
You can either point the first proxy to the second proxy, or point it to the backends directly. Depends if you have firewalls in the way that stop the VPS proxy reaching your backends directly; or if that internal nginx instance is dong anything clever like handling auth, adding headers etc. etc.
In your instance I'd more likely have the VPS locked down and unable to access my internal resources and just open up its access to my internal nginx instance. Therefore chaining proxies would be my approach but there's no right or wrong.