Current rules for sqrt produce NaN for zero primal and (co)tangents

This only happens when the (co)tangent is 0.

julia> using ChainRules

julia> ChainRules.frule((ChainRules.ZeroTangent(), 0.0), sqrt, 0.0)
(0.0, NaN)

julia> ChainRules.rrule(sqrt, 0.0)[2](0.0)
(ChainRulesCore.NoTangent(), NaN)

I suggest we adopt the convention that the produced (co)tangent in this case should also be 0. This is supported by finite differerences:

julia> using FiniteDifferences

julia> jvp(central_fdm(5, 1), sqrt, (0.0, 0.0))
0.0

julia> j′vp(central_fdm(5, 1), x -> sqrt(clamp(x, 0, Inf)), 0.0, 0.0)
(0.0,)

julia> j′vp(central_fdm(5, 1), sqrt ∘ abs, 0.0, 0.0)
(0.0,)

So instead of using @scalar_rule we would explicitly define the frule and rrule.

Start with the existing sqrt rule generated by @scalar_rule and inspect the frule and rrule entry points shown in the issue. Reproduce the zero-primal, zero-(co)tangent cases, then verify that both rules return a zero produced tangent while preserving the shown primal result. Use the FiniteDifferences examples as behavioral checks.