ci: Update RTD sync

[daquinteroflex]

Greptile Summary

This PR enhances the GitHub Actions workflow that synchronizes documentation from the main repository to a Read the Docs mirror repository. The changes add manual workflow dispatch capability, allowing developers to manually trigger documentation syncs and optionally specify a target branch different from the source branch. This provides more flexibility for documentation deployment strategies, testing changes on different branches, and preparing releases.

The workflow maintains backward compatibility - when triggered automatically (via push/tag events), it continues to mirror content to the same branch/tag names as before. However, when manually triggered, users can now specify a target branch parameter to push content from any source branch to a specific target branch in the mirror repository.

Additionally, the PR includes maintenance updates to keep the workflow compatible with current GitHub Actions standards: upgrading from deprecated set-output syntax to GITHUB_OUTPUT environment files, and updating checkout actions from v3 to v4. The logic for pushing to the mirror repository has been consolidated and made conditional based on the trigger type.

The submodule update for docs/notebooks brings in newer notebook content that will be included in the synchronized documentation.

Important Files Changed

File Changes

Filename	Score	Overview
.github/workflows/tidy3d-docs-sync-readthedocs-repo.yml	4/5	Added manual workflow dispatch with target branch parameter and updated GitHub Actions syntax
docs/notebooks	5/5	Updated submodule reference to bring in newer notebook content

Confidence score: 4/5

• This PR is safe to merge with minimal risk as it primarily adds optional functionality and performs maintenance updates
• Score reflects well-structured workflow enhancements with proper conditional logic and backward compatibility preservation
• Pay close attention to the workflow file to ensure the conditional branching logic works correctly in both manual and automatic trigger scenarios

[greptile-apps]

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[daquinteroflex]

@momchil-flex works as per

https://github.com/flexcompute/tidy3d/actions/runs/16723416912

[github-actions]

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