Replace notebooks with Analysis module and .jl example scripts

[logan-nc]

Summary

Closes #156, closes #161.

• Remove all .ipynb files — three run_and_analyze.ipynb example notebooks and the entire notebooks/ directory (spline examples, vacuum tests, equilibrium notebooks)
• Add src/Analysis/ module — reusable post-processing submodule with:
  • Analysis.ForceFreeStates.plot_mode_displacement — Im(ξ_ψ) vs ψ_N for selected m values
  • Analysis.ForceFreeStates.plot_eigenmode_summary — 3-panel DCON summary (eigenvectors, heatmap, eigenvalues)
  • Analysis.ForceFreeStates.plot_stability_criterion — crit vs ψ_N
  • Analysis.Equilibrium.plot_flux_surfaces — R-Z flux surface contours from a PlasmaEquilibrium object
• Convert examples to .jl scripts — each example now has run_example.jl and analyze_example.jl in place of the notebook
• Add PlotlyJS backend — interactive browser-based plots (zoom, pan, hover); plots returned as named variables (p_modes, p_eigen, p_stab) so all persist simultaneously in the REPL
• Preserve CHEASE data — notebooks/CHEASE_INP1/ and notebooks/Chease_Binary_example/ moved to test/test_data/

REPL usage

julia --project=.
include("examples/DIIID-like_ideal_example/analyze_example.jl")
p_modes   # view mode displacement plot
p_eigen   # view eigenmode summary
p_stab    # view stability criterion

Test plan

• julia examples/DIIID-like_ideal_example/run_example.jl completes without error
• include("examples/DIIID-like_ideal_example/analyze_example.jl") opens interactive browser plots
• julia --project=. -e 'using JPEC; JPEC.Analysis.ForceFreeStates.plot_mode_displacement("examples/DIIID-like_ideal_example/jpec.h5")' runs without error
• All existing tests pass: julia --project=. test/runtests.jl

🤖 Generated with Claude Code

[logan-nc]

Summary of notebook content migration

Deleted outright (no content worth preserving)

• notebooks/spline_examples.ipynb + spline_examples2.ipynb — explicitly deprecated per Clean up of Notebooks area #161
• notebooks/vac_fourier.ipynb + vac_wall.ipynb — superseded by Julia vacuum implementation
• notebooks/vacuum_tests/ (entire directory) — references old Fortran paths that no longer exist
• notebooks/equil_chease_binary_test.ipynb, equil_inverse_test.ipynb, equil_soloviev_example.ipynb, equil_lar_example.ipynb — all used deprecated APIs (JPEC.Spl.bicube_eval, old EquilibriumConfig constructor); no test assertions worth extracting
• notebooks/equil_read_chease_comparison.ipynb — visual debugging notebook comparing EFIT vs CHEASE ASCII vs CHEASE binary; same deprecated APIs, no extractable assertions

Moved to test/test_data/

• notebooks/CHEASE_INP1/ (EQDSK, INP1_ascii, INP1_binary, equil.toml)
• notebooks/Chease_Binary_example/ (INP1)

These are equilibrium data files, not code. No tests currently use them, but they are preserved in case someone wants to write CHEASE regression tests later.

Extracted into src/Analysis/

• notebooks/equil_gfile_example.ipynb — the flux surface contour plot logic became Analysis.Equilibrium.plot_flux_surfaces
• examples/*/run_and_analyze.ipynb — the stability plots became Analysis.ForceFreeStates.plot_mode_displacement, plot_eigenmode_summary, and plot_stability_criterion

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Nothing went to benchmarks — benchmarks/ was already clean .jl files and was not touched. No new tests were added either, since the notebooks did not contain any numerical assertions, only plots.