Use ChainRules for operators

Start by reading src/Nonlinear/univariate_expressions_generator.jl and the operator dispatch around src/Nonlinear/operators.jl:570-582. Trace how ReverseAD represents classical, registered, and user-defined operators, then compare that flow with the proposed ChainRules-style dispatch and fallback. Done requires a decided design, updated operator handling, and evidence that the supported cases avoid the current type-instability concerns.

Currently, the approach in ReverseAD is to generate the symbolic expression of the first and second-order derivatives for classical univariate functions using Calculus
https://github.com/jump-dev/MathOptInterface.jl/blob/100eab2e669e73689e1dc214391d97c24402e35c/src/Nonlinear/univariate_expressions_generator.jl
Then, given a representation of the operator as an Int, we do an hard-coded binary search to evaluate a O(log(n)) number of Int comparison instead of a O(n) number of comparison:
https://github.com/jump-dev/MathOptInterface.jl/blob/100eab2e669e73689e1dc214391d97c24402e35c/src/Nonlinear/operators.jl#L570-L582
I'm wondering whether we could get closer to ChainRules instead like other Julia AD framework.
The naive way to do this would be

op = :tanh
f = eval(op)
value_and_derivative(f, 1)

The issue is that, because the value of op is discovered at run-time, the type of f is type-unstable.
But we can use the same trick with the if-else and do

if op == :tanh
    value_and_derivative(tanh, x)
elseif op == :tan
    value_and_derivative(tan, x)
elseif ...
else
   value_and_derivative(eval(op), x)
end

Again, we can do a binary search instead of just a list of if-else.
So, for a fixed number of symbols, we avoid the type-instability thanks to the if-else and we have a fallback for the other ones with the eval.
That would also mean that for registered functions, we need to implement a method and just rely on multiple dispatch instead of adding an operators to the list of user-defined operators, user-defined operators already trigger a type-instability when they are called anyway.