Small update!
I replaced the Sunburst-sugarwater mixture with diluted maple syrup and within a few minutes the colony's activity EXPLODED. I had rarely ever seen them outside during the last weeks, but suddenly up to 20 workers were outside nipping at the feeder from all sides. They soon reduced the outside worker amount to around 5 workers at a time but were outside for several hours during the entire night until the late morning. Now they all look much fatter than before.
Inside the tube not much has changed, they still have a few larvae but I couldn't see eggs or pupae, which isn't really surprising as they're supposed to hibernate.
I did however spot something unexpected - a callow. Looks like despite they're in a colder place now and a lot less active (they barely react to light) they're still raising some brood but at a much lower rate.
I have Lasius Neoniger queen, I also have an omni nest i will move the colony in, but the outworld is smaller than a usual one, will that be a problem? I also really love your colony
Please do NOT force-move them out of their tube, it's not good for them. Small ant colonies, especially when they're of a small species, should stay in test tubes until they fill them out entirely (or move on their own).
Just put their test tube into the omni nest outworld and cover it with a piece of cardboard, they'll be fine (and give them some sand, I found that Lasius love sand - they cover their larvae in it so they can make cocoons and they use it to cover and suppress mold on the cotton). The size of the outworld doesn't really matter while to colony is small, when it grows larger you'll need an additional outworld anyway. You also need a good barrier, people don't mention it often but Lasius ants are really good at escaping.