[Breaking] Use NonlinearSolve for all root finding needs

[avik-pal]

1 downside is that the API for ManifoldProjection will become a bit more verbose, because we are no longer solving a singular root-finding problem (which NLsolve does with pinv IIRC). Instead for in place problems we have to specify resid_prototype, no such restriction for OOP g (yes those are supported now!!).

If the internal solver fails, we terminate the solution process, unlike before where we just keep going.

Initial Benchmarks

For the first test in manifold_tests.jl

# Old Version
julia> @benchmark sol = solve(prob, Vern7(), callback = cb)
BenchmarkTools.Trial: 1054 samples with 1 evaluation.
 Range (min … max):  4.466 ms …  12.455 ms  ┊ GC (min … max): 0.00% … 59.69%
 Time  (median):     4.633 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   4.744 ms ± 745.682 μs  ┊ GC (mean ± σ):  1.74% ±  6.35%

  ▄█▁                                                          
  ███▇▃▃▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▂▂ ▂
  4.47 ms         Histogram: frequency by time        10.6 ms <

 Memory estimate: 1.02 MiB, allocs estimate: 10444.

# This PR
julia> @benchmark sol = solve(prob, Vern7(), callback = cb)
BenchmarkTools.Trial: 6087 samples with 1 evaluation.
 Range (min … max):  558.404 μs …   3.089 ms  ┊ GC (min … max):  0.00% … 54.91%
 Time  (median):     599.674 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   817.805 μs ± 392.500 μs  ┊ GC (mean ± σ):  24.21% ± 23.11%

  ▇█▇▄▃▁                                 ▁▂▃▃▃▃▃▃▃▂▂▂▂▁▂▁       ▂
  █████████▆▅▅▃▃▅▄▁▅▃▃▃▅▁▁▁▁▁▁▁▁▁▁▁▁▁▁▄▄██████████████████▆▇▆▆▆ █
  558 μs        Histogram: log(frequency) by time       1.75 ms <

 Memory estimate: 11.68 MiB, allocs estimate: 11297.

[avik-pal]

Needs SciML/RecursiveArrayTools.jl#356

[avik-pal]

Also ideally needs SciML/NonlinearSolve.jl#382

[avik-pal]

TODO

• Remove Manifest
• Remove SciMLSensitivity from Dependency list

[avik-pal]

Tests pass, I am bumping the project version