refactor: rewrite OverrideInit to be more Zygote compatible

[AayushSabharwal]

SciML/ModelingToolkit.jl#3585 (comment)

[DhairyaLGandhi]

I wouldn't say it's specific to Zygote, but it's also general good practice right? In instances where you cannot determine provenance easily (say you overrode variables with differing types), then also we have to create these copies.

[AayushSabharwal]

Hmm. Sure, I guess. What I find weird is this doesn't work either:

    if initdata.initializeprobmap !== nothing
        u02 = initdata.initializeprobmap(nlsol)
    else
        u02 = u0
    end
    if initdata.initializeprobpmap !== nothing
        p2 = initdata.initializeprobpmap(valp, nlsol)
    else
        p2 = p
    end

    return u02, p2, success

Why is the extra u03 required?

[AayushSabharwal]

Do any other AD frameworks run into this issue? Because if not, it is by definition specific to Zygote regardless of whether this is a code smell or not.

I'm not trying to say Zygote is broken but it would be good to understand this better so we don't keep running into it.