Looking at the outer rim of the Milky Way, I found that on average 13% of star systems have some form of life. This probability seems to remain the same or even slightly increase near the galactic core, when it should probably be significantly lower as you enter the galactic core, due to:
- low metallicity of stars leading to less massive planetary systems/less planets per star on average;
- increased star density leading to more tidal interactions and disruptions of planetary systems over billions of years;
- greater chance of supernovas which render systems sterile,
So this probability should reduce to maybe around 1-2% systems with life inside the galactic bulge.
At the nuclear star cluster at the center of the galaxy, the intense radiation and extreme density of stars should not only render life extremely improbable, but also highly unlikely to even find planets around stars, as the conditions there are very hostile for the very formation of planetary disks, due to tidal interactions with nearby stars, high radiation and low metallicities, such that maybe less than 1% of star systems should even have any planets. (Currently in SE the only star systems you can find without planets are recently formed ones, O type stars and maybe some multiple star systems, no matter where you look 99% of stars have planets).
Nuclear star clusters should also be bigger in general. The NSC in the Milky Way, according to some papers, has a radius of about 4 parsecs, yet in SE has a radius of about 1.2 parsecs. The one in Andromeda should be even bigger, at 12 parsecs, yet is still only 1.5 parsecs in SE.