feat: add Bun package manager support

[synapseradio]

This PR adds support for bun package manager, for which support was added in circleci's node orb in version 7.2.0. CircleCI-Public/node-orb#257

I believe I have followed the same patterns as other package managers here. Please let me know if I've missed anything - we would love to see these changes go in :)

• Add 'bun' to package-manager enum in install.yml and run.yml commands
• Configure conditional logic to use bunx for Cypress commands when Bun is selected
• Leverage circleci/node orb's install-bun capability for Bun installation
• Add Bun example in examples/bun-install directory
• Include Bun configuration in CI test pipeline (.circleci/test-deploy.yml)
• Create documentation example demonstrating Bun usage patterns

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[cypress-app-bot]

• Create a Draft Pull Request if your PR is not ready for review. Mark the PR as Ready for Review when you're ready for a Cypress team member to review the PR.

[MikeMcC399]

@synapseradio

• Add support for Bun cypress#28962 would need to be implemented before this PR could be considered.

[synapseradio]

@MikeMcC399 - thank you for the link and the information.

This PR is only introducing bun as a package manager, but does not suggest it as a runtime as the functionality is decoupled. We've been using such a setup locally for some time back to cypress 13.

When I did the PR to the node orb, I took a similar approach - bun acts as a package manager there, and there is an option to use it as a test runner with certain config, but the orb places no opinion on whether processes run with bun's own runtime over node - that's left to users in how they configure their bunfig.toml / package.json.

I think this is safe to allow here, as I don't believe it introduces a foot gun for these reasons. But, I understand if you consider the support here to be one.

In either case, what would you consider to be next steps for this PR?

Would it be able to move if I were to clarify the example by using npx / adding an explanatory example bunfig.toml that disables bun from replacing node in scripts?

Or, is it something to revisit at a later point? If so, I'd be happy to offer contributions to other places to support.

[MikeMcC399]

@synapseradio

This probably isn't the right place to be discussing whether Cypress supports Bun or not, as it is a complex issue. I'm an external contributor here, so I can't give an opinion representing the Cypress.io team. However since we're on the topic ...

• https://docs.cypress.io/app/get-started/install-cypress#Package-Manager does not list Bun as a supported package manager
• consequently usage instructions, such as https://docs.cypress.io/app/get-started/install-cypress#Install--Run are limited to npm, Yarn & pnpm

I would recommend now waiting for review from the Cypress.io team if they are open to accepting this PR or other PRs related to Bun, for instance in the main cypress repo or the documentation repo. I have requested a review for you.

[synapseradio]

@MikeMcC399 Thank you, man. Totally understand, and I appreciate the pointers and assistance :)