Searching for side chain source track is awesome. Since Logic does not have one and do not list in alphabetical order, it was hard to find the desired source track in a busy project.
Do not know what can be done in Logic but you can download a trial of IZotope RX to fix it.
Here is a quick render of RX which can be better with more detailed adjustments.
App Recording 20240229 0505.mp3
There is no feature like the one in Battery, that is why I still use it a lot but it feels almost EOLed so I do not know how long it will work with new systems so the closest I found is TAL Drum which I like a lot.