At what point does one decides that a microcontroller doesn’t cut it and moves to a full OS system like rpi?

For example this could be an esp32 project

Probably at about the point you look at implementing a network stack on a microcontroller that isn't the ESP32.

Yes, this could have been a ESP32 project, because that has a network stack included, but it doesn't have an LVDS LCD interface, so you're going to have to implement one or the other on any 'simple' microcontroller.

I made a board similar to this that is based on an ESP32 eink screen (the Inkplate, which I highly recommend). The easiest way to render a dashboard like this is with a website, versus making the ESP32 render custom components and call a bunch of APIs). There isn't enough power on the ESP32 to render a website, but there is enough to fetch and render an image, but something has to generate that image. On mine, I use Home Assistant and pre-render a custom dashboard into a PNG, which the Inkplate grabs and renders. This guy skipped all that by just having the Pi do all the work in the first place, which is a fine way to do things if you can get the display working how you like.

If you're producing in volume that's when the microcontroller and effort involved becomes worth the cost savings. For a static screen that just refreshes every 5 mins a tiny MCU can go a looong way. One could do this with 96k of RAM, the data is just text with a few sprites. As a bonus the whole device would consume a few mA on average.