Summary
Gallinari is an elite outside shooter (40% from three over the last three seasons), and an effective midrange shooter as well. As a screener, Gallinari can operate as a pick-and-pop big, but can also take advantage of switches by just shooting over smaller defenders in the mid-post. Gallinari hardly gets to the rim anymore, and while he was never that effective inside anyway, it does make him a bit more one-dimensional offensively. It also causes him to get to the free throw line less often, which hurts him because he's a very good free throw shooter.

On defense, Gallinari has always been below-average, but has been worse than that recently, and is looking like his age is catching up to him. He often has really poor closeouts, and can be a target when trying to defend on the perimeter. Although he's slow-footed, he at least has some size, as he can even operate as a small-ball center against some lineups. Combine his loss in athleticism with the fact that his shooting was slightly down (38% from three) in '21-'22, and it's safe to say Gallinari did not have a great contract year.

Gallinari will be going into his age-34 season in '22-'23, so if he is waived by the Hawks I wouldn't expect him to get any long-term offers, but I think he would get some very solid short-term offers. There's also a chance that a team is willing to trade for Gallinari and take on the last year of his contract, even if it's a bit of an overpay.
 
Cap Considerations
Gallinari's $21.5 million salary for 2022-2023 is only $5 million guaranteed, and if he is waived he will become an unrestricted free agent and the Hawks will have no form of Bird rights on him. The Hawks might waive Gallinari to cut costs to lower their luxury tax bill. However, they would likely first try to trade Gallinari rather than waive him. Even if they waive Gallinari, the Hawks could still try bringing him back using the MLE, BAE (if applicable), or for the minimum. 

If Gallinari becomes a free agent, only teams with cap space would be able to pursue him if his market is above the full $10.3M Non-Taxpayer MLE. However, there's a chance that Gallinari could be had for the full MLE or less, and thus teams without cap space could have interest in him as well.