feat: add explicit cypress install step after dependency install

[mschile]

What

Adds an explicit, package-manager-aware cypress install step that runs after dependency install in index.js.

• npm → npx cypress install
• yarn → yarn cypress install
• pnpm → pnpm cypress install

The package manager is detected by lockfile (the same detection already used for dependency install). The step runs on every install path (including a custom install-command), is skipped when install: false, and respects CYPRESS_INSTALL_BINARY=0.

Why

Package managers may no longer run a dependency's postinstall script by default — pnpm and Yarn Berry (≥4.14) already block them, and npm 12 will via RFC #868. Cypress downloads its binary via a postinstall script, so:

• Cache hit (steady-state CI): binary restored from ~/.cache/Cypress, unaffected.
• Cache miss / first run / cache-key change: the binary was never downloaded and cypress verify failed.

Running cypress install explicitly keeps the binary available on a cold cache regardless of package manager. It's a no-op when the binary is already present, so it's safe to run unconditionally.

Notes for reviewers

• Wired into installMaybe() between install() and listCypressBinaries().
• No core.exportVariable('CYPRESS_CACHE_FOLDER', ...) is needed in the new function — install() always runs immediately before it and already exports it for the process.
• dist/index.js rebuilt via the pre-commit hook (ncc build).
• No unit tests in this repo; behavior is exercised via the example workflows.

Closes #1798

References

• Tracking issue: npm RFC #868 will block this package's install script by default cypress#33980
• Tech brief: cypress-io/engineering-documentation#496

🤖 Generated with Claude Code

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Note

Low Risk
CI install-path change only; respects existing skip flags and is a no-op when the binary is already present.

Overview
Adds installCypressBinary(), which runs an explicit package-manager-aware cypress install after dependency install so the Cypress binary is downloaded when postinstall is skipped (pnpm, Yarn Berry, upcoming npm behavior). It uses the same lockfile detection as install: yarn → yarn cypress install, pnpm → pnpm cypress install, otherwise npx → npx cypress install. It no-ops when CYPRESS_INSTALL_BINARY=0.

installMaybe() now calls this step between install() and listCypressBinaries(); verify/cache behavior is unchanged. dist/index.js is rebuilt to match index.js.

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