Budget
Before anything else, you'll want to figure out how much you're willing to spend on a Galaxy S23 phone case. Value-priced cases continue to improve, so you can find a decent wireless charger for less than $15. But if you're looking for a more premium model, you'll likely have to pay more than $50 and even more for Qi-enabled cases.
Qi Wireless Charging support -- or not?
Most Android phones since the Samsung Galaxy S6 and Galaxy S6 Edge models introduced in 2015 offer inductive wireless charging. Android's standard for these phones is called Qi, and power banks that are fully Qi compatible offer faster charging speeds for Android devices with speeds capped at around 7.5 watts for iPhones. In all cases, you'll need to make sure your phone case is thin enough to allow inductive charging through the back of the phone.
You can save about $8 to $10 by getting a case that doesn't have an integrated metal ring. I generally encourage people to spend the extra money for a Qi-enabled case because of the number of magnetic accessories on the market, some of them quite useful.
Thin or thicker?
Some people like minimal cases that add little to no bulk to their Galaxy S23s, but the majority of people are looking for a case that offers good protection -- or even maximum protection. I tell people to find a case that's not too thick and maybe even pretty slim and that offers at least 6-foot drop protection (and good corner protection).
Do you want a clear case?
Clear cases are popular because they show off your phone (and its color). Clear cases, especially cheaper ones, can become less clear over time and slowly start to yellow. Many case makers now add UV protection to their clear cases to prevent yellowing.