KingOfTheHood It doesn't sound like the app is being killed but rather they're wrongly expecting to keep a connection open without running a foreground service to keep the app active.
JackBauer01170 Inactive apps have their execution quickly frozen on Android. If they want to be active in the background, they need to use standard OS mechanisms to run code in limited amounts in the background at an interval, under certain conditions, etc. If they want to remain active they need a foreground service. The app is incorrectly written if it has issues with this.
it stopped running background syncs
This is a buggy app.
'Suspend execution of cached apps'
Set this to 'disabled'
This will substantially reduce your battery life by enabling every app cached in memory to freely run as much as it wants while the device is awake. Any app waking the device to do work via structured methods will allow all apps cached in memory to run and every app cached in memory will be able to run while you're using it. You almost certainly don't want to do that. Apps are supposed to properly use the structured ways of running in the background. If they need to run continuously, they should be using a foreground service.
Both of the issues described here are blatant app bugs which would occur on the stock Pixel OS or other modern Android versions too. The app developers should fix the bugs.