Aarun: Robust latent-embedding/PCA analysis across seeds

[MartinAstro]

Extend the embedding/PCA analysis so conclusions are not based on a single random initialization.

Expected output:

• Collect multiple seeds and trajectories for the embedding/PCA plots.
• Test whether visual patterns persist across random initializations.
• Investigate whether latent encodings can be mapped back to original state-space features for interpretability.
• Document the conclusion with figures and a short explanation of what the visualization does and does not prove.