The higher the octane, the greater the resistance to detonation (often called knock or ping). Engines with higher cylinder pressures (such as boosted or high compression engines) need higher octane fuel so the fuel doesn’t ignite under pressure in the cylinder before the spark plug even fires. That can lead to a lot of damage.
Engines have knock sensors that can catch the detonation before it becomes an issue, and cope with the lower grade fuel by retarding ignition timing within reason. Since they do only “recommend” 89 for the 5.7, it would lead me to believe there is a performance and economy benefit in running higher grade fuel, but no harm would be done if you run 87. The engine can likely pull adequate ignition timing to run satisfactorily on 87. Only caveat would be if you’re pulling heavy or operating in very hot weather…I think the mid-grade would be a good idea to maintain good performance and a bit of a safety margin.
With the 6.2 or any other boosted or high compression engine, you can really run into trouble not running premium as there is simply not the safety margin needed. The cylinder pressure of this engine under boost is far too high avoid detonation issues on lower grade gas. The old “pull timing” trick has it’s limits before you start burning valves and cats, or the engine just doesn’t run at all. So you can’t count on the computer to defy physics and save your ass.
As long as you mind the distinction between recommended and required, you’re okay.