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When Julius Caesar implemented the calendar named for him, it famously included a system whereby February was occasionally extended by 24 hours.

Existing Roman timekeeping systems were constructed around a February containing exactly 28 days, for cultural reasons.  Further, there was a notable civic holiday celebrating the founding of the Roman republic, "Regifugium," and that holiday was tied to the calendar date "March -4" culturally (Roman dates were always counting down to something), which I think is similar to how the founding of the American republic is tied to the calendar date "July 4;" any future calendar for the United States will almost certainly have a "July," and it will be at least 4 days long.

The new calendar system was implemented in such a way that "March -4" was effectively 48 hours long.  It appears the original intent was for the countdown of days  to March to be "-5, -4b, -4, -3..." so that the feast of Regifugum was held on the "real" March -4, the latter of the two days.  After Christians adopted the Julian Calendar, March -4 was chosen to be the feast date of Saint Matthias, whith the apparent intent that Matthias be similarly celebrated on the "real" March -4 on leap years.

(Examples of the Christian use of Roman dating habits:  Christian tradition has John the Baptist being six months older than Jesus.  The feasts of their respective births are July -6 and January -6.)

Over centuries, the custom of effectively using negative numbers for calendar dates gave way to using positive numbers.  The date of the Christian feast of Saint Matthias became known as "February 24," with the apparent intent that the feast be observed on "February 25" during leap years.

But there were schisms of various sizes over time and isolated parish priests typically had more pressing concerns than a quadrennial footnote.  Due to failures of communication and understanding, different parishes in different Christian sects celebrated Saint Matthias on different days during a leap year.

The modern solution to this problem?  I don't think any major Christian denomination currently schedules anything during the last five days of February ("just to be sure," to borow from Ellen Ripley).  (But I would argue that the Gregorian Calendar's "ecclesiastic new moon" in February 2020 was on February 25, not February 24...)

Anyway...

Since 1972, the last minute of a Gregorian Calendar month can be 59, 60, or 61 seconds long (and God help us all if this happens to February in a leap year!).  Due to faliures of communication and understanding, software developers adhered to a cultural tradition of all minutes being 60 seconds long.  Time servers adjust the lengths of different "seconds," and different servers adjust different "seconds" by different amounts, to maintain the sacred 60-count in a way that is literally out-of-sync with each other.  I think this is somewhat similar to how the length of March -4 was smeared, and eventually different people smeared it in different ways. 

At the time Julius Caesar was working on the new calendar, the Egyptian calendar used a "Sothic" year with a fixed length of 365 days.  The Julian Calendar was developed with the help of Egyptian astronomy and the Egyptian astronomer Sosigenes, but the leap year system was only implemented in Egypt after the conquering Augustus Caesar imposed it.