refactor!: split out preparation

[gdalle]

Warning

Breaking changes.

Breaking changes

• Split out preparation into a function prepare_implicit to simplify ImplicitFunction (not yet documented)
• Modify linear_solver specification
  • modify IterativeLinearSolver, remove IterativeSolvers dependency
  • replace \ with DirectLinearSolver
• Remove keep_input_type from OperatorRepresentation

Non-breaking changes

• Replace block solver with individual solver in ForwardDiff

Still to do

• Document preparation
• Warn against nesting
• Decide if the prepared chain rules are valid since there is mutation

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Files with missing lines	Coverage Δ
ext/ImplicitDifferentiationChainRulesCoreExt.jl	95.23% <100.00%> (+0.23%)	⬆️
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	96.26% <100.00%> (-3.74%)	⬇️
src/implicit_function.jl	100.00% <100.00%> (+11.53%)	⬆️
src/preparation.jl	100.00% <100.00%> (ø)
src/settings.jl	100.00% <100.00%> (ø)

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.