Restructure tests

[gdalle]

CI

• Replace 1.6 and 1.11 with the new adaptive version keywords lts and pre

DI tests

• Replace the folders Single and Double with Back

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 58.33333% with 5 lines in your changes missing coverage. Please review.

Project coverage is 96.89%. Comparing base (f27415c) to head (3bf82cd).

Files	Patch %	Lines
DifferentiationInterface/test/runtests.jl	58.33%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #354      +/-   ##
==========================================
+ Coverage   96.81%   96.89%   +0.07%     
==========================================
  Files         101      101              
  Lines        4839     4830       -9     
==========================================
- Hits         4685     4680       -5     
+ Misses        154      150       -4     

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