This web page gives detailed instructions for making a wormery using either wooden or plastic boxes.  There are many ways of making wormeries – this design uses gravel in the bottom layer to aid drainage – this will probably help to prevent the drain tap from blocking too.

https://homefarmer.co.uk/building-and-using-a-wormery/

Taps are a weak point in most wormery designs – they often get blocked by dead worms, slugs, snails or other grunge.  A 22mm pipe (from a DIY shop or plumbers’ merchant) dripping into a plastic bottle or a watering can is often a more trouble-free drainage outlet than a water-butt tap – it’s not as if you ever really need to turn the wormery drain tap off (in fact doing so is a recipe for drowned worms!).