It is not logical to say that a state of affairs now exists (wet street at this time) during the time that something else has been happening (no rain for some time). " It's easier to detect the dissonance when the tenses are even more incompatible. " For the durational use of "while" you need to coordinate the tenses of the two clauses so that one activity or event takes place completely within the time period of some other activity.
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Plus, if the sentence were like "The street is wet, while it is not rainy", is it possible to take "while" as "although"?