Burgess is fine
It may be old stock from Pets at Home. It's a good mix for dwarf hamsters. The Bunny Dream Expert is a great mix but as you say it means ordering from Zooplus whereas Burgess is available more easily.
As we never know what storage conditions are like for hamster food it is a good idea to freeze it for a week first. When I haven't had time I stick the bag in the freezer and take some out each day while it's still in the freezer
So each day it's been frozen a bit longer and 24 hours will help. Then take the whole bag out after a week and put itor the contents in a lock and lock box - I use those because they are the only ones supposed to full air tight.
At least they weren't moths! The main reason people freeze the food first is to prevent an outbreak of moths, which I have had and took months to get rid of! It is very common from pet foods. They contain moth eggs which aren't visible to the human eye - it's unavoidable and fairly normal and only an issue when the conditions are right for the eggs to hatch - and then any moths can proliferate by laying eggs all over the place. They are a particular type of moth called a food moth or pantry moth. Freezing for a week kills the eggs so then you know it won't happen! But I still store the food in an airtightcontainer anyway after freezing so if anything did hatch it can't get out!
The little bugs won't do your hamster any harm but if you do see a moth in the cage I would suggest a full clean out of the cage - not normally recommended but nips it in the bud.
Yours doesn't sound like moths though as you wouldn't see anything and moth larvae when hatched don't look like you've described.