Pico is a bit advanced for beginners, even WiFi version requires some custom code to connect to the network, and running anything complicated like a web server dumps you into hyper-optimized embedded software development.

Raspberry Pi Zero runs the same Linux as your desktop PC and comes with WiFi, you simply run Python on it and you can make a web server with all bird feeder controls you need, and you can install VPN if you're paranoid, it will handle most tasks except AI.

NanoPi Neo comes with Ethernet connector but no WiFi for pretty much the same money and very similar specs, plus faster CPU.

OrangePi Zero has both Ethernet and WiFi but a few cents more expensive.

All three have tons of manuals and sample code on the net, and most code working on Raspberry Pi will work on OrangePi or NanoPi with some minor change to load a differerent GPIO library (the interface is compatible, so your code stays the same)

So you pick the peripherals and the connectivity you need.