https://i.imgur.com/Jk0vFfO.png
So here we can see that botanical nurseries do not allow you to select modules for beacons for some reason. (probably because botanical nurseries have 0 module slots themselves). However, they DO allow you to utilize beacons for speed/efficiency. As seen in the following pic:

https://i.imgur.com/1H1cXWE.png

Suggested fix: Allow beacons to select modules based on buildings "allowed modules categories" even if building has zero module slots itself.

Thanks for reading!

It's not just the allowed module categories. Need to the check the crafting machine's effect receiver (if assigned). And see if uses_beacon_effects is enabled.

https://lua-api.factorio.com/latest/classes/LuaEntityPrototype.html#effect_receiver

https://lua-api.factorio.com/latest/concepts/EffectReceiver.html