Make SearchProperties probes robust to non-primitive Real eltypes (AD)

[ChrisRackauckas-Claude]

Please ignore until reviewed by @ChrisRackauckas. Draft — opened by an agent.

Problem

Constructing SearchProperties on a ForwardDiff.Dual-valued knot vector throws a MethodError:

MethodError: no method matching Float64(::ForwardDiff.Dual{...})

ForwardDiff.Dual <: Real, so it dispatches to SearchProperties(v::AbstractVector{<:Real}), whose sampled linearity / uniformity / log-linearity probes coerce intermediates with Float64(...). Float64(::Dual) is deliberately undefined. This surfaces downstream when an interpolation is reconstructed inside ForwardDiff and both values and knots are promoted to Duals (e.g. SciML/DataInterpolations.jl#557).

Fix

The Float64(...) coercions are redundant for the primitive eltypes — for Int/Float32/Float64 the probe expressions are already Float64. Removing them and computing in native arithmetic:

• makes the probes work for any ordered Real (classification is taken from the primal, partials are preserved), and
• leaves the Int/Float64 hot path byte-for-byte unchanged.

I verified ForwardDiff defines unsafe_trunc(Int, ::Dual), so once the probe stops calling Float64, the closed-form UniformStep search path also works end-to-end and derivatives propagate correctly.

Tests

Adds a regression testset differentiating through both values and Dual-valued knots (uniform + non-uniform), plus a full Auto search over uniform Dual knots checked against Base on the primal. Wires ForwardDiff into the test targets.

• Full GROUP=Core suite: 171,933 pass locally.
• Runic clean.

Relation to other work

This unblocks SciML/DataInterpolations.jl#557 — with this merged, that PR can drop its _default_search_properties/_search_properties opt-out helpers and just bump the FindFirstFunctions compat bound. A separate PR handles a distinct pre-existing Rational crash in the UniformStep kernel found while testing eltype robustness.