updating notebooks

[FilipeFcp]

Updating notebooks for using web.run and ModeSimulation

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Note

Low Risk
Changes are limited to example notebooks/documentation code paths and should not affect production libraries, but may break tutorial execution if the new APIs are misused.

Overview
Updates the example notebooks to use the newer web.run workflow and ModeSimulation APIs.

This modernizes the notebook execution patterns to match current client behavior, reducing drift between the notebooks and the recommended simulation setup.

^{Reviewed by Cursor Bugbot for commit 7658e9a. Bugbot is set up for automated code reviews on this repo. Configure here.}

[github-actions]

Spell Check Report

TFLNTidy3d.ipynb:

Cell 38, Line 1: 'voltage-dependent'
  > Next, we run the voltage-dependent mode simulations with `web.run`.

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Checked 5 notebook(s). Found spelling errors in 1 file(s).
Generated by GitHub Action run: https://github.com/flexcompute/tidy3d-notebooks/actions/runs/26050074443

[alec-flexcompute]

Great update as usual @FilipeFcp ! One thing: in RadiativeLossesModeSolver.ipynb cells 9, 11, 13, 19, 21, 24, 27, and 29 maybe use web.run instead of web.Batch for consistency

[jungmin-flex]

Looks good to me too!

[FilipeFcp]

Thanks @alec-flexcompute
I updated the notebook, and added another one.

[alec-flexcompute]

Looks good, thanks!