Are hospital based retrospective cohort studies subject to Berkson's Bias?

Hi this is a bit of an elementary question but I’ve been having trouble wrapping my head around it.

As a hypothetical example, say I had hospital administrative data from a large geographic area, such as a whole state. My goal is to see whether a history of smoking is associated with an increased risk of in-hospital mortality among patients hospitalized for COVID-19.

Would Berkson’s bias be a potential problem in a scenario like this? Could having a history of smoking make you more likely to be hospitalized with COVID, and those who are hospitalized might be more likely to die? Or is this not Berkson’s bias but some other type of selection bias? I feel like I usually hear of Berkson’s bias in regard to case-control studies that use hospital controls, but I’m wonder if there is a similar concept for hospital based retrospective cohort studies? What other types of bias might someone want to look for in a scenario like this? I’ve tried looking up studies but many do an unsatisfactory job of explaining this.

wouldn’t you do some kind of matching to reduce bias?