We do not currently have the ability to detect a Kardeshev 1.0 civilization at Alpha Centuari. Here is a paper showing Alpha Centuari has infra-red emission close to a K1.5 civilization. Emissions from a K1.0 would be completely lost in the noise.This is developing into yet another game of Astronomical Top Trumps. There is always some parameter that can put an astronomical object near the top or near the bottom of a list.
The milky way is what it is. Now, if someone could come up with something relevant about whether Galactic size might relate to Alien Civilisations (other than some pro-rata rule) then that could be interesting.
There is some evidence that Kardeshev 2.0 civilizations are rare in a galaxy like the Milky Way at the Sun's radius. A single data point does not convey any statistical information about galaxies in general.
For a "top galaxies" category the Milky Way and the Orion Spur could still be close to the top in terms of quality. It appears that it is not yet infected with species that over-consume all potential resources. The Milky Way might still be in a fairly pristine state.
There is a survey of galaxies looking for KIII civilizations using data from WISE. Out of around 105 sources the authors recommended 95 of them for further study. 5 have been studied some. The other 90 were not studied at the time of publication. In order to make that list a civilization needs to capture more than 50% of the galaxy's starlight (or produce energy equal to starlight). Colonizing 80% of the stars in a galaxy and using on average 63% of individual star's light would still count the galaxy as uncivilized. Also galaxies where 100% of F,G,K, and M stars had colonies with 95+% energy utilization but most of the A,B,O stars did not have colonies would have been counted as uncivilized too.
There is effectively no data about the civilizations in galaxies except for the solar system containing Earth.