Julia 1.6 compat

[gdalle]

Make everything compatible with Julia 1.6

• Add Compat.jl and PackageExtensionCompat.jl to dependencies
• Use PackageExtensionCompat.jl to do Requires.jl on all extensions
• Use stack freely because it is Compat.stack
• Replace destructuring (; x, y) = obj with @compat (; x, y) = obj
• Replace @kwdef with Base.@kwdef
• Widen compat bounds
• Make JET, Aqua and JuliaFormatter stuff conditional on VERSION >= v"1.10"
• Pkg shenanigans to get around the fact that no registered version of DI / DIT is 1.6 compatible yet (that's the fucking point)
• Install the backends in the test code itself for DI, in two batches depending on 1.6 compat

Only FiniteDifferences, ForwardDiff, ReverseDiff, Tracker and Zygote are tested on 1.6

This is a bit hard with every backend at once: we need to figure out how to split the tests

• https://discourse.julialang.org/t/different-test-dependencies-according-to-julia-version/113767
• https://discourse.julialang.org/t/how-to-test-package-with-different-sets-of-test-dependencies/113478

See also this problem with stdlib compat:

• https://discourse.julialang.org/t/compat-bounds-for-stdlib-and-empty-intersection-issue-on-ci/105898/2?u=gdalle

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 99.46809% with 1 lines in your changes are missing coverage. Please review.

Project coverage is 95.43%. Comparing base (571133f) to head (0b862db).

Files	Patch %	Lines
...onInterfaceChainRulesCoreExt/differentiate_with.jl	50.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #243      +/-   ##
==========================================
+ Coverage   95.32%   95.43%   +0.10%     
==========================================
  Files          74       74              
  Lines        3936     3942       +6     
==========================================
+ Hits         3752     3762      +10     
+ Misses        184      180       -4     

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