We don’t general follow “science” in halachic matters
We follow science as handed down by the Chachmei Hamesorah.
Shmuel’s Tekufa isn’t Sept 24, it is Oct 7 (until 2100 when it will be Oct 8)
That said , there is a more accurate Tekufa of Rav Ada Which was shortly before midnight Sunday Sep 25 which is obviously closer to 9/22 than Oct 7 is *
The Chazon Ish explains that the reason why we don’t use it for vesein tal umatar is that it is too complicated for the massess. We all need to figure out when to say vesein tal umatar, same goes for birchas hachama. So we use a simpler albeit less accurate calculation that is “close enough” (He explains that Shmuel isnt arguing on Rav Ada, of course Shmuel new his calendar was innacurate in Berachos he says he knew the paths of stars like the roads of Neharda)
However for the calendar which is given over to chachamim we use the more complicated tekufa of Rav Ada
*
The reason why this is off by more than you might expect, is that Jewish Tekufos assume 4 equal periods
That of Shmuel assumes 365 days & 6 hrs or 365.25 days a season is 1/4 of that = 91 days 7.5 hr
That of Rav Ada assumes a year lasts 365.24682 days a season is 1/4 of that
(For comparative purposes The Gregorian Calendar assumes a year lasts 365.24250 days (Note this too is a bit too slow and will eventually need to be adjusted as the calendar is sliding forward by one day every 3323 years))
However the astronomical seasons are not of equal length. This is becasue the Earth’s trip around the sun is not a crcle it is an ellipse so the seasons are not equal I found these values online: Spring = 92 days, 19 hours; summer = 93 days, 15 hours; autumn,= 89 days, 20 hours; winter= 89 days, zero hours. Thus while the Gregorian and Astronomical YEARS are very close to that of Rav Ada. The SEASONS are off by a few days