⚔️Serberia

Generally, I see the main reasons for visiting the slums as follows:
1) If you have to go there as part of a specific quest. For example, from a guy with a basilisk.
2) If you want to check out the black market. It's possible that this is an alternative way for Alessia to get a book on summoning demons.
3) To check out "The Clanging Steel".
4) To check out the green events in the cheap hotel and at the local iteration of Ikigai.

Added 1 minute ago

The cat will probably die. Or run away, or move out, or betray us.

It will tear Eugene's throat, seize power in the city, and announce its accession to Royental.