Add forward enzyme rules for init and solve

[sharanry]

• Followup to #377

TODO:

• [ ] Test against other algorithms
• [ ] Error on unspported algorithms.

[codecov[bot]]

Codecov Report

Merging #416 (0935919) into main (b9da6ac) will decrease coverage by 1.11%. The diff coverage is 0.00%.

@@            Coverage Diff             @@
##             main     #416      +/-   ##
==========================================
- Coverage   64.94%   63.83%   -1.11%     
==========================================
  Files          26       26              
  Lines        2068     2099      +31     
==========================================
- Hits         1343     1340       -3     
- Misses        725      759      +34     

Files	Coverage Δ
ext/LinearSolveEnzymeExt.jl	0.00% <0.00%> (ø)

... and 1 file with indirect coverage changes

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[ChrisRackauckas]

This looks like a real test failure.

[sharanry]

@ChrisRackauckas The test failures seem unrelated.