There's already a lot of variation in the proportion of dark matter to visible matter in different galaxies. Revising one galaxy doesn't change the statistics that much.
(However you are right that from a Bayesian point of view, the Milky Way is the galaxy we have the most data on. So should count for a lot more than a random galaxy.)
Yes, that’s the basically the reason this paper gives for the large discrepancy between their estimate of the mass and prior estimates. The Gaia satellite measured the positions and velocities of billions of stars in the Milky Way, information we’ve never had before, so a new estimate being significantly different from the prior estimate is not _that_ surprising.
But the 5% number that I quoted above should not be taken as an extremely precise number. You can plainly see that it has only one significant figure; if the real number turns out to be 4% or 6% then I don’t think cosmologists will be too surprised.
(However you are right that from a Bayesian point of view, the Milky Way is the galaxy we have the most data on. So should count for a lot more than a random galaxy.)