Initial support of AutoDiff through SAP

[amcastro-tri]

Definitely we should provide full AutodDiff support through SAP, with analytical gradients through the solver, work already started by @joemasterjohn.
However, this issue tracks a very preliminary support of AutoDiff for SAP such that we at least match the level of support provided by TAMSI. This in order to support the migration towards SAP becoming the default discrete solver, per discussion here.

The solution we'd like
TAMSI today provides AutoDiffXd support (modulo geometry support) using dense linear algebra.
We'd like SAP to at least provide this same level of support.

Alternatives we've considered
When using SAP (for either of the approximations kSap, kLagged, kSimilar) with and AutoDiffXd plant, SAP defaults to a dense solver (instead of the supernodal solver) and we perform automatic differentiation using the implicit function theorem within the non-linear Newton iteration, the same way that TAMSI does it today.

Additional context
This is to support the migration to SAP as the default discrte solver, issue #19322.
Also, removal of deprecated APIs, #21225.