When you combine them, you get a beautiful and literal image: “The old state (故态) again (复) sprouts (萌).” This botanical metaphor suggests that bad habits are like weeds; even if you pull them, the roots can remain dormant, ready to sprout again at the first opportunity.
The idiom 故态复萌 taps into a universal human experience: the difficulty of genuine, lasting change. In a Chinese cultural context, it often connects to the concepts of self-cultivation (修身, xiūshēn) and perseverance. Achieving change is a constant effort, and a relapse is a common, though disappointing, part of the journey. A close Western equivalent is “Old habits die hard.” Both idioms express the difficulty of changing ingrained behaviors. However, there's a subtle difference in imagery.
故态复萌 is a common idiom used in both spoken and written Chinese. It's almost always used with a negative or critical connotation. You use it to describe a relapse into a bad habit or undesirable state.