The main point is that when you desire no things outside of your control ( like life, health … ) you encounter no „unhappiness“ or when you desire only Virtue you get „complete“ happiness.
It simply doesn't work that way. It's impossible to completely "not worry" about certain basic needs. Their absence will always worsen the quality of life. According to the Stoics, theoretically, even if you were stranded on a lonely island, you would be "happy," but that's simply impossible. It will always lead to negative psychological consequences. To some extent, it is also impossible to choose to desire virtue exclusively. Fundamental desires are by their nature such that they cannot be removed by a simple change of judgment.
This argument about virtue only works if we define happiness in isolation from feelings of pleasure. It seems to me that defining happiness this way is rather inappropriate. If someone is in a state where they don't experience even a shred of pleasure, they will never say they are "happy". Intuitively, through introspection, one can see that happiness is largely related to pleasure.
The Stoics believe that pleasure has no significance. From this perspective, we can indeed acknowledge that happiness is possible when we focus solely on virtue. Since happiness consists solely in fulfilling our rational nature, and this rationality is within our power, we cannot experience any failures. Although there are some reservations in this respect as well. The aforementioned virtue is not solely dependent on us. To be guided by virtue, one requires a proper bodily state. To achieve this state, one must strive to fulfill desires that are not inherent in virtue.
An example of one such desire is the desire to eat. If you don't eat, your rational faculties will inevitably weaken in favor of your instincts. To engage in virtue at all, you must first have the material prerequisite. And this material prerequisite is not strictly within the individual's will. It is not dependent on our control. Hence, other philosophical schools, such as the Peripatetics, did not consider virtue to be self-sufficient.