Fix cache updates

[gdalle]

It seems that some Cache types from FiniteDiff are not updated correctly before derivative evaluation at a new point. See also:

• FiniteDiff with :central includes junk DifferentiationInterface.jl#983
• fix jacobian(_, AutoFiniteDiff(fdjtype=Val(:central))) DifferentiationInterface.jl#987

[ChrisRackauckas]

@oscardssmith were you tracking this? Or should I take it?

[oscardssmith]

if you can take it that would be good. I think the DI issue should give enough info for Claude to 1 shot

[gdalle]

Beware that just because the issue arose on a specific field (x1) of a specific cache (JacobianCache) in a specific mode (:central) doesn't mean it's not more widespread