Question: "Would someone help to understand the accuracy of the calculated 'Delta T' against the numbers provided on the websites."
The nature of Delta T (ΔT) reflects an irregularly-fluctuating natural phenomenon: it is a quantity that fundamentally has to be observed and measured, rather than calculated.
Evidence suggesting that mean solar time is after all somewhat irregular -- and not uniform as had been long believed -- began to be accumulated from about the mid-19th century onwards. During the 1920s and 1930s the evidence for this irregularity came to be generally accepted as convincing. The first timescale independent of the fluctuations of mean solar time ("Ephemeris Time") was devised in the late 1940s. The Wikipedia article on Ephemeris Time gave (as of late 2015) a reasonably good account of the history. Some of the linked articles are also useful, including the article on Delta T, but the current version of the article on Delta T has unfortunately been amended to include a misleading suggestion that Delta T is a product of calculation -- some older versions, still accessible through the history tab, were more accurate.
Since the fundamental values of Delta T are products of observation, of course these intrinsically belong to the past -- even if sometimes a very recent past. The historical values of Delta T vary in accuracy, from very high accuracy for the past few decades, maybe to 0.0001 second as at the US Naval Observatory website, to much lower accuracies for centuries-old dates, for which Delta T had to be estimated (recently) from a variety of old historical observations. (See especially the historical work of Stephenson, Morrison and Hohenkerk, e.g. at (http://astro.ukho.gov.uk/nao/lvm/)).
Naturally, present-day time-users tend to wish for current quantities rather than history. So, attempts are regularly made to predict Delta T for the near future. The results of these attempts are at best approximate. This can be seen from graphs that compare past predictions with what then turned out to be the actual measured quantities.
An example is the second out of three graphs shown at the web-page for "Delta T : Past, present and Future" on the "Astronomical Almanac Online" website here. This shows "Current values and short term predictions of Delta T" from 2000 to 2022 -- including the odd and unexplained fact that in the interval 2020-2022 the measured values of Delta T stopped trending upwards, and have even slightly diminished. The graph shows clearly how quickly and how much the actual measurements began to deviate from both of two sets of calculated predictions. One set is of IERS predictions made for about 2006 onwards (which turned out lower than actual, about 2 seconds lower by 2022). Another set is a series of USNO predictions (which turned out higher than actual, over 2 seconds higher by 2022).
For a long time, the US Naval Observatory website was a good source of the latest data and predictions about Delta T. But in the last two years and more, its webpages were sometimes inaccessible, and data for latest measured values and most recent predictions seemed to be updated either seldom or not at all. But recently I found that I could again access updates, now via (https://www.cnmoc.usff.navy.mil/Organization/United-States-Naval-Observatory/Earth-Orientation-Department/USNO-Earth-Orientation-Products/Long-term-Delta-T/) and its links to:
"Monthly values of (TT - UT1) since 1973. Updated quarterly" -- here are the latest few entries at the time of writing this:
> Date (TT-UT1, secs)
> 2021 10 1 69.2893
> 2021 11 1 69.2880
> 2021 12 1 69.2908
> 2022 1 1 69.2945
> 2022 2 1 69.2913
and to the latest "Predictions of (TT-UT1) from the present through 2027. Updated annually." -- here are a few entries for the period about the time of writing this:
> Year TT-UT1 (s) Uncertainty (s)
> 2021.25 69.358221 0.000004
> 2021.50 69.351422 0.000003
> 2021.75 69.41 0.12
> 2022.00 69.48 0.16
> 2022.25 69.57 0.22
> 2022.50 69.63 0.27
> 2022.75 69.65 0.33
> 2023.00 69.73 0.40
It can be seen, even from these two brief table-quotes, that even the expert predictions, maybe only about a year or two old, have already begun to deviate appreciably from the actuals. The IERS website gives essentially the same data, but it divides Delta T into components given on different web-pages. The USNO combined format -- when available -- seems much the most convenient. I suggest that websites showing values other than these, however they may have been calculated, should be regarded as approximations; but the best of them include some very useful approximations for past Delta T values, for example calculated by formulae that define a collection of spline-curve segments, saving the volume and inconvenience of large lookup tables while losing negligible amounts of accuracy.
