Not sure but it might help...
I have a 2004 Ford Ranger, same symptoms. Turns out it was the fuel pump.
Also, I have had several mustangs, recently my 05 GT would hesitate and shudder at idle. On a recent road trip a small tick from the front of the engine developed. Turns out one of the plastic chain guides broke in half. I spent 100 bucks on amazon and replaced all of the timing components in two days. Runs like new now. No codes ever showed up. Turns out the chain guides and cam phasers are prone to failure. Something to think about.
In any case, I would do two things if I were in your shoes.
1. Try the soapy water spray bottle technique to see if you have an engine leak.
2. If that doesn’t work, spend the 14 bucks on an auto stethoscope and poke around the timing cover to see if you hear any clicking.
Just my .02. Hope you figure it out.