He's definitely stressed, and you should not be handling him right now at this point in time.
I already posted about the round cage in your other thread, but that could be contributing to his stress.
Since he's such a new budgie (also, he's not four weeks old-- at four weeks, budgies don't even have all their feathers yet! He's at least 8-10 weeks old at minimum), he needs two weeks to settle in on his own without you trying to touch him or take him out.
After two weeks, you can start putting your hand near his cage to get him used to it, then put your hand in the cage without moving, then moving it closer over time. All of this will take weeks, not days, so it's important to have patience.
The wing trembling and "skinny" body appearance is characteristic of stressed budgies.
Playing calm music in the background and talking to Lilac in soft, reassuring tones will help him start to settle in.
Best of luck!