Rough Idle and rattling noise

Ive having a really rough idle with ratting noise. I heard its usually cause by jumped timing and bad tensioners so I took off the valve covers to inspect them and they are the 3rd gen tensioners and they look to be in ok shape, but they are fairly easy to compress them down which Im not sure is bad or not. No codes except P1578 which is for the throttle body.Im not sure what to do or look for now, any ideas?

You might need to replace secondary Timing chains, if the timing was off a Tooth you would have bent valves.
I just had to end the relationship sold 2- 2000 S type Jaguar for $500. one was for spare parts and other was driven until a spun bearing.