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This article reminds me a lot of the book "A Fire upon the Deep" by Vernor Vinge.

While reading this article and viewing the diagram of the Milky Way, I wondered, does time pass more slowly from the point of view of those bodies near the center of the galaxy, which are moving more quickly?

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Of course the faster you go the slower time passes but you have to travel at least 30% the speed of light to make a dramatic difference. See the table here:

http://www.emc2-explained.info/Time-Dilation-at-Low-Speeds/

Also: the star with the shortest known period orbiting our central black hole travels no faster than 1% the speed of light.

https://en.wikipedia.org/wiki/S0%E2%80%93102

Peak stellar speed observed as "nearly 3% the speed of light":

https://www.nature.com/articles/d41586-018-05825-3

which appears to be rounded up from actual 2.55% value:

https://en.wikipedia.org/wiki/S2_(star)#May_2018_pericentre_...

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