A number (cathode) is lit by pulling it to ground so the current can flow. Other cathodes are either left floating or pushed up to a high enough voltage to stop the flow of current, e.g. 75V
To control the brightness, you need to switch the current on and off quickly. This is typically done using some kind of PWM of whatever is controlling current flow.
If you still want a power supply that allows you to control the voltage from software, I recommend the Taylor HVPS power supplies, or you can incorporate my design if you want to build it from scratch (it also allows voltage control from software) http://www.nixies.us/projects/nixie-tube-power-supply/
Good luck!
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...SNIP...
BTW. I've started my journey with ESP8266 very recently and I'm a newbie to the NTP topic. How often can I check the time at a server to be not considered a spammer? Is once per hour okay?
It uses WiFiManager to set up the connection from the ESP to a router (I strongly recommend WiFiManager, Actually I use ASyncWifiManager because I use the ASyncTCP libraries). In doing so, it gets the user's location from the browser and then uses google's location APIs to get the timezone data. The net result is that it uses NTP to get UTC time, and then automatically adjusts it for the timezone/DST in the user's location.It looks like the user can override the location if they want to.