Solved point-source runtime profiling + cluster breakdown solved steps (#657 phase 3)

[Jammy2211]

Summary

Phase 3 of PyAutoLens#657: likelihood-runtime profiling for the solved (centre-free) point-source fit variants. Adds runtime siblings for FitPositionsImagePairAllSolved (+RepeatSolved steady-state entry) and FitPositionsSourceSolved under the results/runtime/<class>/<model>/ convention, and extends both cluster likelihood-breakdown scripts with solved-fit per-step entries on the standard cluster model. Headline: the analytic β* step costs ~timing-noise-level overhead per likelihood call (image-plane net +3% across systems; source-plane +9–30% on sub-0.1s eager fit totals) while removing 2 free parameters per point source from the non-linear space.

Scripts Changed

• scripts/point_source/likelihood_runtime/image_plane_solved.py — NEW sibling: lower/compile/first-call/steady-state timings for FitPositionsImagePairAllSolved, plus a FitPositionsImagePairRepeatSolved steady-state entry; results at results/runtime/point_source/image_plane_solved/
• scripts/point_source/likelihood_runtime/source_plane_solved.py — NEW sibling for FitPositionsSourceSolved; full pipeline JITs cleanly (xp bug fixed in phase 2 / PyAutoArray#414); results at results/runtime/point_source/source_plane_solved/
• scripts/cluster/likelihood_breakdown/image_plane.py — adds FitPositionsImagePairRepeatSolved per-system fit-total steps + solved-vs-plain delta summary ("solved" JSON block; original step totals preserved)
• scripts/cluster/likelihood_breakdown/source_plane.py — adds plain FitPositionsSource and FitPositionsSourceSolved per-system fit-total steps (apples-to-apples) + delta summary
• scripts/misc/likelihood_runtime/README.md — two new table rows

Committed results (v2026.7.23.1, quiet-machine sequential runs): runtime JSON+PNG for both solved siblings, refreshed cluster breakdown JSON+PNG (now with solved steps), and the cluster simulator summary regenerated by the current simulator (the previous local dataset predated scaling_galaxies.csv).

Upstream PR

PyAutoLabs/PyAutoLens#659 (merged 2026-07-27).

Test Plan

• All four scripts run green sequentially on a quiet machine; pinned-value regression checks pass
• Source-plane breakdown cross-checks step-by-step likelihood vs the reference fit (MATCH rtol=1e-4)

Generated by the PyAutoLabs agent workflow.