That is only a small part of the data, just 25 years worth of satellite data. There are ground measurements going back almost 150 years. Using all the data shows a clear acceleration:

https://climate.nasa.gov/vital-signs/sea-level/

The comment about coming out of an ice age is also not relevant - sea levels have indeed been rising since then, but nowhere near the current rate, so the current increase is mostly unrelated to that. For example:

https://www.giss.nasa.gov/research/briefs/gornitz_09/

Twentieth century sea level trends, however, are substantially higher that those of the last few thousand years.

Your first link has the essentially same data as what I referenced - 3.2 mm per year recently. Since 1919, they show a rise of about eight inches. The current rate amounts to 12 inches per century.

Your second link is interesting - thanks! It’s not different from what I said. We have come out of an ice age. The interglacial epochs have been historically relatively short.

Sorry, perhaps I wasn't clear. The first link I gave has two graphs. The top one indeed has the same data you linked to - the 25 year satellite record. The second link is the one I was actually referring to though - that is the almost 150 year record including tidal gauge data. There is a pretty clear acceleration there. The earlier rate is lower than the later rate - in fact you even said that too (12" vs 8"). So I am a bit unclear why you said originally there was "no acceleration in the rate"?

This article supports your claim (pdf):

Climate-change–driven accelerated sea-level rise detected in the altimeter era

https://www.pnas.org/content/pnas/115/9/2022.full.pdf

I think that fitting a quadratic to such a short run of data is premature, and that extrapolating that same acceleration for 80 years is tendentious. However, the paper is otherwise interesting, and I hope they do an update in ten years and include their previous prediction :-)

Yes, that's the article I was thinking of, good find!

Agreed the extrapolation is debatable.

What is most astounding to me is that they are able to measure not just an increase of 3mm a year in sea levels by satellite, but that the data are precise enough that they can determine the change in this rate. The precision of the instrumentation and processing required to measure to that level of precision is astounding.