If you do not want the chickens to be included in your system as either assets or inventory, then the proper way to put the eggs into inventory is to do the “Material Receipt” method.
If you want the chickens to be ‘production assets’ then they could be considered collectively as a workstation for producing eggs. In this scenario you would create a production order for the number of eggs you collected. Feed would be the raw material moved to the chickens with a “Material Transfer for Manufacturing” and the completion of the production order would automatically generate the “Material Transfer” from chickens to the default warehouse for the eggs.
If you wanted to track the productivity of individual chickens they would each be an asset and you would divide the amount of daily feed by the number of chickens for raw materials per chicken. Then you create production orders per chicken for the eggs collected from each chicken that day. This would generate a large number of production orders and transfers.
I know it sounds crazy the deeper you dig down into the concept, but ERPNext is a fair system for managing production. However with the constant variability of chickens and eggs only really makes sense if you just create Material Receipt stock entries to put the eggs into the inventory warehouse. Any process other than this seems to create a bunch of busy work in ERPNext that would likely only take away your valuable time from running the farm.