Simplify tutorial and README

[adrhill]

• replace @repl blocks by @example blocks to reduce visual noise (fewer julia>, ; and newlines)
• this is me being opinionated, but I opted for using ADTypes instead of import ADTypes
• use several backends in README example to make the point of this package overly obvious
• minor additions to tutorial

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 95.60%. Comparing base (0f71a42) to head (de68eaa).

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #216   +/-   ##
=======================================
  Coverage   95.60%   95.60%           
=======================================
  Files          73       73           
  Lines        3820     3820           
=======================================
  Hits         3652     3652           
  Misses        168      168           

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[adrhill]

I will make some more changes to this once #217 is merged.

[gdalle]

it is merged, you can track all the places in the docs where ADTypes is used and remove them

[adrhill]

Ready for review!

[adrhill]

@gdalle A test on coloring currently fails:

Coloring: Test Failed at /home/runner/work/DifferentiationInterface.jl/DifferentiationInterface.jl/DifferentiationInterface/test/coloring.jl:11
  Expression: maximum(row_colors) < size(A, 1) ÷ 2
   Evaluated: 51 < 50

Stacktrace:
  [1] macro expansion
    @ /opt/hostedtoolcache/julia/1.10.2/x64/share/julia/stdlib/v1.10/Test/src/Test.jl:672 [inlined]
  [2] top-level scope
    @ ~/work/DifferentiationInterface.jl/DifferentiationInterface.jl/DifferentiationInterface/test/coloring.jl:508

[gdalle]

It's a randomized test, should nearly never fail. Fix the seed and call it a day for now