Add new backends with DifferentiationInterface.jl #682

Job	Run time
Julia 1 - ubuntu-latest - x64 - pull_request	12m 16s
Julia 1 - windows-latest - x64 - pull_request	14m 9s
Julia lts - macos-latest - x64 - pull_request	12m 25s
Julia lts - windows-latest - x64 - pull_request	9m 17s
Julia 1 - macos-latest - x64 - pull_request	17m 52s
Julia pre - ubuntu-latest - x64 - pull_request	12m 0s
Julia lts - ubuntu-latest - x64 - pull_request	8m 47s
Julia pre - macos-latest - x64 - pull_request	11m 52s
Julia 1 - macos-15-intel - x64 - pull_request	20m 15s
Julia 1 - ubuntu-24.04-arm - arm64 - pull_request	11m 43s
Julia 1 - macos-latest - arm64 - pull_request	6m 56s
Julia lts - macos-15-intel - x64 - pull_request	9m 23s
Julia pre - windows-latest - x64 - pull_request	13m 47s
	2h 40m 42s

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