Hm, it does indeed sound odd. It sounds a little like labored breathing to me, with a little ‘click’.
I’ll bet your budgie also does this in the daytime, but it’s not as obvious when they’re moving around. Also, if an illness is not in more advanced stages, they might not present with symptoms 100% of the time, keep in mind. By the time a budgie is in more obvious stages of illness, it is often too late.
Your budgie does need to be seen by an avian vet soon, to determine if there is an illness, and how to make it better. Please keep up posted!