Depends, the Eagles don't need Slay's permission to simply restructure a deal. A simple restructure is just a cap accounting trick. In that sense a restructure still means Slay gets his $17 million owed this year just the timing of the payment is different.
For all intents and purposes, when you see "restructure" reported in the news, it's a simple restructure. A maximum restructure if often just called an extension. The Eagles likely won't do a basic restructure because the void years are already high. And I suspect them letting him look for a trade partner is, in part, a way to see what the market might dictate in terms of an extension. Teams looking to acquire him are likely going to want to sign him to an extension.