Cache SearchProperties per interpolation to skip per-call Auto probes

The previous commit migrated the sorted-batch evaluators to FFF 2.0's
strategy-dispatched `searchsortedlast!` API, but called it with the
default `strategy = Auto()`. Each such call has `Auto()` re-probe the
knot vector `A.t` for linearity / NaN / uniformity on every batched
evaluation. Because `A.t` is fixed at interpolation construction, that
probe is wasted work on every call after the first.

This commit precomputes `FindFirstFunctions.SearchProperties(A.t)`
once at cache-construction time and stores it as a new
`t_props::propsType` field on every interpolation cache struct, then
threads `FindFirstFunctions.Auto(A.t_props)` into each batched
`searchsortedlast!` call site so the probe is skipped.

Changes:

  - `src/interpolation_caches.jl`: every cache struct
    (`LinearInterpolation`, `QuadraticInterpolation`,
    `LagrangeInterpolation`, `AkimaInterpolation`,
    `ConstantInterpolation`, `SmoothedConstantInterpolation`,
    `QuadraticSpline`, `CubicSpline`, `BSplineInterpolation`,
    `BSplineApprox`, `CubicHermiteSpline`, `QuinticHermiteSpline`,
    `SmoothArcLengthInterpolation`) gains a `propsType` type
    parameter and a `t_props` field, populated by
    `FindFirstFunctions.SearchProperties(t)` in the inner constructor.
  - `src/integral_inverses.jl`: same change for
    `LinearInterpolationIntInv` and `ConstantInterpolationIntInv`.
  - `src/interpolation_methods.jl`: every
    `FindFirstFunctions.searchsortedlast!(...)` call site in the
    sorted-batch evaluators now passes
    `strategy = FindFirstFunctions.Auto(A.t_props)`.
    `_eval_interior_adaptive!` gains a `strategy` parameter so the
    Akima call site can pass the cached strategy through.

For `AbstractRange{<:Real}` knot vectors the `SearchProperties`
specialised constructor skips every probe (all properties are known
statically), so the construction cost is zero. For `Vector{Float64}`
the populated constructor runs an O(n) NaN scan once at construction
time; for integer / non-numeric eltypes only the O(1) sampled-
linearity probe runs.

Tests: all five groups pass locally on Julia 1.11:

  Core       |  2539 pass, 5 broken (pre-existing)
  Methods    | 42151 pass
  Extensions | 13178 pass
  Misc       |    11 pass
  QA         |    18 pass

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

Author: ChrisRackauckas

src/integral_inverses.jl

@@ -33,17 +33,19 @@ Can be easily constructed with `invert_integral(A::LinearInterpolation{<:Abstrac
   - `t` : Given by `A.I` (the cumulative integral of `A`)
   - `A` : The `LinearInterpolation` object
 """
-struct LinearInterpolationIntInv{uType, tType, itpType, T} <:
+struct LinearInterpolationIntInv{uType, tType, itpType, T, propsType} <:
     AbstractIntegralInverseInterpolation{T}
     u::uType
     t::tType
     extrapolation_left::ExtrapolationType.T
     extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
+    t_props::propsType
     itp::itpType
     function LinearInterpolationIntInv(u, t, A, extrapolation_left, extrapolation_right)
-        return new{typeof(u), typeof(t), typeof(A), eltype(u)}(
-            u, t, extrapolation_left, extrapolation_right, Guesser(t), A
+        t_props = FindFirstFunctions.SearchProperties(t)
+        return new{typeof(u), typeof(t), typeof(A), eltype(u), typeof(t_props)}(
+            u, t, extrapolation_left, extrapolation_right, Guesser(t), t_props, A
         )
     end
 end
@@ -93,19 +95,21 @@ Can be easily constructed with `invert_integral(A::ConstantInterpolation{<:Abstr
   - `t` : Given by `A.I` (the cumulative integral of `A`)
   - `A` : The `ConstantInterpolation` object
 """
-struct ConstantInterpolationIntInv{uType, tType, itpType, T} <:
+struct ConstantInterpolationIntInv{uType, tType, itpType, T, propsType} <:
     AbstractIntegralInverseInterpolation{T}
     u::uType
     t::tType
     extrapolation_left::ExtrapolationType.T
     extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
+    t_props::propsType
     itp::itpType
     function ConstantInterpolationIntInv(
             u, t, A, extrapolation_left, extrapolation_right
         )
-        return new{typeof(u), typeof(t), typeof(A), eltype(u)}(
-            u, t, extrapolation_left, extrapolation_right, Guesser(t), A
+        t_props = FindFirstFunctions.SearchProperties(t)
+        return new{typeof(u), typeof(t), typeof(A), eltype(u), typeof(t_props)}(
+            u, t, extrapolation_left, extrapolation_right, Guesser(t), t_props, A
         )
     end
 end