We are all trying to get peace of Spain and remember, Spanish monarchy pretty much left Spain. If they are smart they'll probably deescalate and focus internally. Until now it looked like they are smart and there not much they can do in Spain anyway as it will either be in British, or French hands. No point in fighting others wars when they know that Spain is lost, but empire remains!
Edit: they are in no state to fight a prestige war, they can strike back at their enemies only in long term, but in short term they must swallow their pride .
Can't get Spain back but they can still hurt the British in other ways like the British land in the New World.
I mean it's true, but they have advantageous position similar to US and time.
US for one is quite far from the point where it will be able to extert American hegemony, not to mention it got itself involved in world politics (despite the lucky rolls and memes this war will probably cost US far more than victory will) and other potential threats like British for example are busy with more pressing matters like Europe, India and US. French are the same , they are busy with Europe and if they win they will spend decades in integrating their European conquest.
Basically new Spain is good for now.
Actually given their losses in Americas and victories in India/Spain, plus situation in France it's quite possible for them to accept white peace and refocus on conquest of India, putting Americas back in place and integrating their Spanish conquest in Portugal to create decent buffer in Iberia.
After all we all know peace is temporary, but we also know that both sides need it.
I'd rather think they don't want peace the British or even the French. The more they recover the harder it will be to beat them later. I'd say peace benefits the British more than the French.