revamp!: use KrylovKit for type flexibility (beyond Vector), split out preparation

[gdalle]

Warning

Breaking changes

Breaking changes

• Switch IterativeLinearSolver to KrylovKit, hide settings from the public API for now
• Remove flattening and reshaping and buffering since KrylovKit preserves types and handles higher-order arrays
• Remove OperatorRepresentation settings since the operator A is now just a function
• When computing Jacobians with Zygote, one may have to set strict=Val(false) because it doesn't backpropagate the right tangent type
• Remove preparation-related stuff from the ImplicitFunction constructor, put it in a separate function prepare_implicit (private for now)

Non-breaking changes

• Add type stability tests

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Files with missing lines	Coverage Δ
ext/ImplicitDifferentiationChainRulesCoreExt.jl	95.45% <100.00%> (+0.21%)	⬆️
ext/ImplicitDifferentiationForwardDiffExt.jl	100.00% <100.00%> (ø)
src/ImplicitDifferentiation.jl	100.00% <ø> (ø)
src/callable.jl	100.00% <100.00%> (ø)
src/execution.jl	100.00% <100.00%> (+3.73%)	⬆️
src/implicit_function.jl	100.00% <ø> (ø)
src/preparation.jl	100.00% <100.00%> (ø)
src/settings.jl	100.00% <100.00%> (ø)
src/utils.jl	100.00% <ø> (ø)

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