Yep I think it's about time I replaced the other two oxygen sensors. The car has started to hesitate under load again so I think it's only going to get worse.
I have retrofitted cruise control so I don't get any warnings on the trip computer screen. Funny enough I didn't get a check engine light either, but the light still works because it comes up on the pre-start check.

 

I don't know if I understand it correctly (as I am from Poland), but the message says "CRUISE NOT AVAILABLE". Not "cruise control".

So I'm assuming it concerns driving in general and means "sorry, your jag is damaged, cruising is not recommended today, I'm limiting revs to 3000 to prevent damage".

As for your problem, I'm not sure what to do. P0037 and P0057 is indeed oxygen sensors problem, but these sensors are (as far as I know) not responsible for fuel trims. They only check catalyst converter efficiency.

 

I think that becuase i have retrofitted my cruise control, nothing comes up on my display. Happy to be corrected by that. But I'm also pretty sure I don't have the display which tells you all sorts of things about the car, only the odemeter screen.
Yep I think maybe the car detected actual knock or ping because the oxygen sensors are giving the wrong readings, so maybe there's too much fuel going into the mixture and not combusting properly? Therefore the car limited itself to 3000RPM.
The car is working okay now and I've just been on a 250km trip with it too. But I think I'll sleep better if I get those oxygen sensors replaced. I replaced one faulty oxygen sensors before and this made the car much happier, the hesitation is a sign that one or both of the other sensors must be on their way out too.

 

It seems like you just don't have "message center". There should be lights on instrument cluster instead of displayed messages, then.
Message center was optional, probably unrelated to cruise control. With navigation module present it also displays route messages.
If mixture is off by 20% then you will have revs limited to 3000 and OBD errors (for example P0171 and P0173 if it is too lean)
You can use OBD reader to check errors as well as current fuel trims (mixture correction).

But chances are, that your oxygen sensor errors are enough to enable rev limiter, and replacing sensors will help.

PS. The sensor you've replaced is sensor 1 - the one responsible for mixture correction. Without it there is no correction at all. No doubt your car it is happier now