Deprecation removal contact_solver

[jwnimmer-tri]

The MbP has some deprecations related to the contact solver:

drake/multibody/plant/multibody_plant.h

Lines 2235 to 2238 in f8f957f

	DRAKE_DEPRECATED(
	"2024-04-01",
	"Use set_discrete_contact_approximation() to set the contact model "
	"approximation. The underlying solver will be inferred automatically.")

drake/multibody/plant/multibody_plant_config.h

Lines 64 to 73 in f8f957f

	/// Use discrete_contact_approximation to set the contact model approximation.
	/// The underlying solver will be inferred automatically. The deprecated code
	/// will be removed from Drake on or after 2024-04-01.
	std::string discrete_contact_solver{""};
	// TODO(amcastro-tri): Along the removal of discrete_contact_solver on or
	// after 2024-04-01, update the default value of
	// discrete_contact_approximation to be non-empty. The value will be either
	// "similar" or "lagged", to be decided based on the information we collect
	// from our users.

Normally I'd just remove the deprecated code myself, but I can't this time because I don't have the "information we collect from users".

Please remove the deprecated code / comments and adjust the nearby code as-necessary.

[jwnimmer-tri]

I think probably this ticket is holding up #21095, so I hope to have us resolve this sooner than later.

@amcastro-tri As of today, which of "similar" or "lagged" (or "sap?) is our best guess at the most useful default value? I can open the PR if you like, I just don't know which one to choose.

[amcastro-tri]

Per f2f: running kLagged would be ideal in that it does not introduce artifacts results of the convexification (i.e. "gliding" when sliding). However, kLagged introduced a "weak" coupling of friction and normal forces that might impact the perfomance (meaning predicted success/failure) of grasping tasks in simulation. In this regard, kSimilar is the safe bet, in that it solves most of the big issues we had with kSap and introduces Hunt & Crossley for the accurate and stable modeling of dissipation.

See #21294, thus far a WIP until we confirm all tests pass. I run a few tests locally and they succeded. Lets wait for Drake CI and Anzu CI for the final veredict.

[jwnimmer-tri]

@amcastro-tri Would you like to add this to our project board, for yourself?