Change binding energy derivative calculation from Symbolics to FastDifferentiation

[elaine-ran]

1. Since FastDifferentiation.jl is much faster than Symbolics.jl and the executables made by FastDifferentiation.jl are also faster, change𝓔′ from using Symbolics to FastDifferentiation. Resolves issue #26 ! a. This required the addition of a type of PNSystem, called FDPNSystem() which stores its state variables as FastDifferentiation.Nodes. FDPNSystem() must be initialized with a float type (ex. FDPNSystem(Float64)).
2. To account for these changes, update the binding_energy.jl test file to test 𝓔′ using FDPNSystem(Float64) instead of SymbolicPNSystem().
3. Move all usage of Symbolics into an extension PostNewtonianSymbolicsExt.jl.

[moble]

Almost working. Should be easy to get the last errors fixed, but I have to run for now. Here's what I've done so far:

• I realize now that we can't get rid of Symbolics entirely just yet, because var_collect — which is a critical piece of @pn_expansion — depends on Symbolics. For now, I'll just pretend the the extension is a normal file, in hopes of being able to change it to a real extension sooner than later.
• I made a lot of changes to main since you started your fork, so I've rebased your changes.
• As part of those changes, I fixed type instabilities; as part of that I had to move constructors inside the NSNS and BHNS structs, so for consistency I did that with BBH and FDPNSystem.
• I removed a bunch of little things that made it into your commits accidentally
• CI complains if the dependencies and compat in Project.toml aren't in alphabetical order, so I reordered them
• Docstrings need to be directly above the thing they're documenting, with no extra newline in between, or they just appear to be some random string, so they disappear immediately
• Extension methods (like type_converter(::PNSystem{T}, x) where {T<:Vector{Symbolics.Num}}) don't need to be documented again if they just extend a function that was already documented in the main code.
• Moved unhold to the extension along with hold.
• Need to rename old 𝓔′ to 𝓔′Symbolics to avoid conflicts
• Because the extension is a separate module, the names from the main package module have to be imported, as do PostNewtonian itself, and MacroTools.

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 64.28571% with 30 lines in your changes missing coverage. Please review.

Project coverage is 82.50%. Comparing base (865de96) to head (689dba7). Report is 3 commits behind head on main.

Files	Patch %	Lines
ext/PostNewtonianSymbolicsExt.jl	38.09%	26 Missing :warning:
src/systems.jl	87.50%	2 Missing :warning:
src/utilities/macros.jl	50.00%	2 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #48 +/- ## ========================================== + Coverage 82.32% 82.50% +0.17% ========================================== Files 26 27 +1 Lines 894 926 +32 ========================================== + Hits 736 764 +28 - Misses 158 162 +4 ```

:umbrella: View full report in Codecov by Sentry.
:loudspeaker: Have feedback on the report? Share it here.

[moble]

Thanks Elaine! Nice work!