Calendar year versus Tropical year
Leap seconds don't correct for the problem of the calendar years cumulatively drifting out of sync with the seasons, which is what the first source means with 365.2425 being inequal to 365.242374. Instead, the purpose of leap seconds is to correct the problem that 24 * 60 * 60 = 86400 seconds is not the length of the day, and the reason we don't get leap seconds nicely on schedule is that the slowing of the Earth's rotation is nonuniform.
What the second source means when talking about the slowing of the Earth's rotation, is that when the day gets longer, the length of the tropical year in days gets shorter, which means that the relative error between the mean calendar year and the tropical year gets even worse.
The cumulative error in the calendar is not corrected by any means currently, and it will take a long time for the error to be meaningful in the sense of impacting everyday life, so it is not viewed to be a real problem now. This might change in a couple of thousand years, or then people even then might value the algorithmic stability of an unchanging calendar more than the spring equinox's occurence near March 20th.