perf(animator): cache the spring settle time

[LeadcodeDev]

Severity Low, category quality. Location: crates/rustmotion-core/src/engine/animator.rs:470

Impact

spring_value is reached per animated property, per node, per frame (box_builder.rs:538 -> resolve_props_for_effects -> resolve_animation_value_full, animator.rs:997). When SpringConfig::duration is set, each of those calls runs a full coarse scan plus 40 bisection steps, with steps clamped to [2000, 20000]. For the shipped defaults (stiffness 100, mass 1 -> omega 10, period 0.628 s) desired_steps is 2292, so one animated property costs ~2333 exp/sin/cos evaluations per frame to recompute a value that depends only on (damping, stiffness, mass, rest_threshold) — completely invariant across frames. A 30 s/60 fps render with 20 nodes carrying two spring-duration properties each burns roughly 165 million redundant solver evaluations. The function's own doc comment acknowledges it is "called on every spring_value sample when duration is set".

Fix

Memoize spring_settle_time on the quantized (damping, stiffness, mass, threshold) tuple in a thread-local HashMap, or precompute time_scale once when the SpringConfig is resolved and carry it on the resolved animation instead of recomputing it inside spring_value.

Evidence the audit read

let natural_rest = spring_settle_time(
                damping,
                stiffness,
                mass,
                threshold,
                MAX_SPRING_SEARCH_SECONDS,
            );
---
    let steps = desired_steps.clamp(SPRING_SETTLE_MIN_SAMPLES, SPRING_SETTLE_MAX_SAMPLES);
    let dt = max_t / steps as f64;
    let mut last_exceed_idx: usize = 0;
    for i in 0..=steps {

Stacked on fix/gradient-angle, which carries the previous finding of this workstream. GitHub shows only this finding's diff; merge in order.

Part of the September 2026 audit remediation chantier. Refs #220 (RM-37).