Is expiation obligatory for someone who vowed never to eat sugar at all, then it became clear to him that his intention was specific to sugary sweets, while he continued to drink tea with sugar based on his initial understanding, and then discovered that the vow also included sugar in drinks?

If, by your vow, you intended to abstain from sugary sweets, then you have not broken your vow by putting sugar in tea. This is because the reference point for a vow (nadhr) and an oath (yameen) is the intention of the one making the vow or oath. Scholars have explicitly stated that an oath is based on the intention of the one swearing it, and a vow is like an oath, with intention being the governing factor. Furthermore, vowing not to eat sugar falls under the category of vowing to abstain from something permissible (mubah). The majority of scholars hold the view that a vow concerning a permissible act does not become binding, and no consequence results from not fulfilling it. This is in contrast to the view of Imam Ahmad, who believes it is binding and requires expiation (kaffarah) if not fulfilled.