Add EigenvalueProblem support with dense, Arpack, ArnoldiMethod, KrylovKit, and JacobiDavidson backends

[AJ0070]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

• Added an EigenvalueProblem abstraction analogous to LinearProblem, with solve dispatch and shared spectral selection (which, sigma).
• Added DenseEigen (default, via LinearAlgebra.eigen) plus ArpackJL, ArnoldiMethodJL, KrylovKitEigen, and JacobiDavidsonJL backends as package extensions.
• Added genuine factorized shift-and-invert for KrylovKit, and fixed Arpack generalized problems and the iterative default_nev.
• Added guarded tests covering every backend.

Define a problem, pick (or auto-select) an algorithm, and call solve, giving eigenvalue computations the same experience as linear solves. Standard (Av = λv) and generalized (Av = λBv) problems are supported, with shift-and-invert for interior eigenvalues near sigma.

JacobiDavidson is wired up for standard problems only (upstream jdqz is broken) and targets eigenvalues nearest the shift.

Addresses #143.
AI Usage: Used GPT 5.5