The Yankees, who have had Eovaldi once already and are therefore familiar with him, are not likely to give up an MLB-ready prospect like Clarke Schmidt to acquire an expensive SP with questionable durability. Eovaldi only netted Tampa Jalen Beeks when he did not have $34mill left on his deal. Doubtful he gets a better pitching prospect plus a young controllable MLB slugger now with that money attached.
They'll hand the ball over to Schmidt first. If he doesn't work out, they can just demote him back to the training site. If they trade him and Eovaldi struggles or gets hurt, they cannot undo the trade and get Schmidt back...