GEOPY-2544: Add mechanics to re-start inversion if results are present in the SimPEGGroups

[domfournier]

GEOPY-2544 - Add mechanics to re-start inversion if results are present in the SimPEGGroups

[Copilot]

Pull request overview

This PR aims to enable “resume/re-start” inversion workflows by making optimization / directive logic less dependent on iter == 0 and by preventing first-iteration outputs from being rewritten when prior results already exist (e.g., in SimPEGGroups / GeoH5 outputs).

Changes:

• Adjust optimization initialization and stopping-criteria baselining to better support resumed runs (and tweak iteration print formatting precision).
• Update GeoH5 saving directives to avoid writing iteration-0 outputs on non-zero opt.iter, and refine how data entity types are handled when writing.
• Improve directive behavior for scaling misfit multipliers and ensure Dask inverse problems recompute residuals when missing.

Reviewed changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated 6 comments.

Show a summary per file

File	Description
simpeg/optimization.py	Changes iteration printing precision and alters optimizer iteration / baseline initialization to support restart/resume flows.
simpeg/directives/_sim_directives.py	Refactors cross-gradient scaling to accept an explicit model argument and calls it from endIter.
simpeg/directives/_save_geoh5.py	Skips writing iteration 0 on resumed runs and adjusts entity type handling when writing GeoH5 data/logs.
simpeg/directives/_directives.py	Updates ScaleMisfitMultipliers to support restarts and adds a cooling factor concept plus higher-precision logging.
simpeg/dask/inverse_problem.py	Ensures residuals are recomputed when absent even if the model hasn’t changed.

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