No they won't, it's a post-June trade. The cap hit proration would hit next year's cap. They'd gain cap space back this year, but probably take around a $60M dead money bath next year. However, if Payton wants to get out of that deal, maybe he takes Mac off our hands and gives us Jeudy and a pick to sweeten the exchange.
Essentially, if they trade him now they are only responsible for the signing bonus proration that they've already got against their cap for this year, and they gain back a percent of his salary that becomes the responsibility of the team that acquires him, and the acquiring team also becomes the responsible party for his 2024 guaranteed salary. Then the other $60ish million of signing bonus proration hits 2024's cap. If they keep him and cut him next year, they still take that $60M dead money bath plus another $17M of dead money due to his 2024 guaranteed salary. If they keep him past the 5th day of the 2024 league year, his 2025 salary also becomes guaranteed, which is $37M. So they could potentially be on the hook for another almost $120M if they keep him through next year, or only $60M if they can find a trade partner now. That $60M swing is why they might be the ones needing to sweeten the pot.