Lean into bang-bang convention

[gdalle]

Core

• Accept the bang-bang convention fully: mutation may never happen
• Make pushforward!!/pullback!! depend on pushforward/pullback
• Change jacobian!! to make sure we write back into the column with the results. Wrote this part with a manual loop because copyto! allocates for array views
• Move things around in core files

Docs

• Reinsert "preparation" section

Tests

• Fix title of correctness tests that said call count
• Remove mutation tests

Extensions

• Remove useless code for out-of-place backends
• Add experimental Taped.jl support

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 88.33333% with 14 lines in your changes are missing coverage. Please review.

Project coverage is 91.67%. Comparing base (e2e04ae) to head (a54d60d).

Files	Patch %	Lines
...erfaceTapedExt/DifferentiationInterfaceTapedExt.jl	0.00%	7 Missing ⚠️
src/jacobian.jl	92.30%	4 Missing ⚠️
src/DifferentiationTest/printing.jl	0.00%	1 Missing ⚠️
src/DifferentiationTest/test_operators.jl	0.00%	1 Missing ⚠️
src/backends.jl	50.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #92      +/-   ##
==========================================
- Coverage   92.59%   91.67%   -0.93%     
==========================================
  Files          49       50       +1     
  Lines        1243     1201      -42     
==========================================
- Hits         1151     1101      -50     
- Misses         92      100       +8     

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