Add package manager list and installation instructions

[MikeMcC399]

• closes Add explicit package manager support list and installation instructions #6092

Issue

Get Started > Install Cypress information for using package managers: npm, Yarn and pnpm is scattered and not at the same level of detail for each package manager. Developments in package management usage, such as the introduction of Corepack, are not covered. When Yarn is mentioned there is no distinction made between Yarn 1 Classic and Yarn Modern. For the latter there is no indication about which nodeLinker modes are supported and which do not work.

Change

• Generalize package manager installation and refer back to each package manager's own documentation.
• For Yarn Modern prefer node-modules and exclude Yarn Plug'n'Play for Component Testing usage.

Corepack comment

• Since Corepack is currently considered as experimental by the Node.js documentation site, do not refer to Corepack explicitly.
  • npm does not use Corepack.
  • Yarn Classic was released before Corepack and does not document its use at all.
  • Yarn Modern has its own separate Corepack page.
  • pnpm has a Corepack section as part of the Installation page

pnpm 10.x comment

• Delay adding any specific information for pnpm 10.x until the documentation and releases have stabilized.

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