Remove custom printing

[gdalle]

Following SciML/ADTypes.jl#64, there is no more need for the custom printing utilities in DI.

DI source

• Remove backend_str, replace backend_package_name with package_name (with a much simpler implementation that extracts "Something" from "AutoSomething(...)".
• Fix display of SecondOrder and DifferentiateWith

DI docs

• Remove uses of backend_str

DIT source

• Remove uses of backend_str

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 75.00000% with 3 lines in your changes missing coverage. Please review.

Project coverage is 96.73%. Comparing base (bb0d874) to head (984cf5c).

Files	Patch %	Lines
DifferentiationInterface/src/utils/printing.jl	71.42%	2 Missing ⚠️
DifferentiationInterface/src/utils/exceptions.jl	0.00%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #332   +/-   ##
=======================================
  Coverage   96.73%   96.73%           
=======================================
  Files         101      101           
  Lines        4865     4840   -25     
=======================================
- Hits         4706     4682   -24     
+ Misses        159      158    -1     

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