Software updates worsen your battery

No.

But what can happen is an update may trigger some re-indexing or other background maintenance tasks so you could see a hit on your battery for a day or two. Not all do that, but really this is not something to worry about.

The battery on my 12 mini was performing really badly ( discharging completely from 100% overnight, overheating all the time) so I was holding off iOS updating for fear of making it worse. I made a Genius Bar appointment to get the battery replaced and they told me to install the latest update in advance of this. Did it yesterday and ( don’t want to speak too soon/tempt fate but) it appears to have fixed the battery issue!

Unless there's some kind of runaway process on the device. How quickly is it draining? and how does that compare to your usual use?