I've built quite a few VFD clocks and one with a display similar to yours. In fact it is quite an obsession of mine. The main (but certainly not the only) difficulty you'll have with writing replacement firmware for that ready made clock is reverse engineering the schematic including display connections and working out how to use the VFD driver chip(s) on it. For the rest, there are enough ESP clock projects around as a starting point and anyway you really only need a few lines of code (if you hard code the WLAN credentials, time zone etc.). Of course it is better to also run a web server on it for such configuration settings.
Here are couple from my collection (sorry about the picture quality). The smaller one I made quite recently and documented here: ESP32-C3 Supermini clock with VFD display
