Backport bug and test fixes to release-0.10 to prepare for new 0.10 release

[devmotion]

This PR backports the following PRs from the master branch to the release-0.10 branch such that they can be released:

• #586
• #615 (backport requested in https://github.com/JuliaDiff/ForwardDiff.jl/pull/615#issuecomment-1946030042)
• #631
• #683
• #688 (for the test fixes)
• #687 (backport requested in https://github.com/JuliaDiff/ForwardDiff.jl/pull/710#issuecomment-2382903198)
• #703 (fixes https://github.com/Ferrite-FEM/Tensors.jl/issues/219)
• #708

The PR extends and replaces #710 (note that tests fail in #710 since eg fixes from #688 and #703 are missing).