The Torah designates the beginning of the year of counting months from Nissan, so Adar is the end of the year 12th month. We must make Pesach in the spring as it says Chag Haaviv, so when they noticed that Pesach did not come out in the spring, at the time when Rosh Chodash was designated through witnesses, another month was added, see Rambam Hilchas Kidush Hachodash (4,1). On Purim Katan we don’t say למנצח which is interesting since we don’t find too many times when we don”t say it, but ‘זה הקטן גדול יהי there is a potential for it to be Purim Gadol by not adding a leap year month.
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