Ok so complain to the ops department that they need to unify their logs. That's their problem, not yours. If the company is big I would expect them to be doing that anyway, either they coalesce around a journald-type thing that aggregates the logs locally, or they'll use another centralized service like datadog, splunk, etc. Edit: If you are ops then this is your entire wheelhouse, you should be able to solve it at scale without messing everything up.
It has been my career experience that 5+ digit employee companies more resemble Chiba City than they do the USS Enterprise.
"Give me an IP, username and password - what OS is it?" are about all you start with and go from there. It's probably a critical system to someone, and everyone swears on a stack of bibles that nobody did anything, touched anything or made a change. You have very specific domain knowledge (kernel, grub, SAN/storage, systemd, dbus, etc.) and typically ask a lot of questions to the systems owner as your fingers are flying ruling out reasons (low hanging fruit common issues).