refactor(package-manager)!: extend the API and provide access to spawn child (#18576)

# Why

Fixes ENG-7545

This proposal PR changes the API of the (node) package managers, with
the goal of:

refactor(package-manager)!: extend the API and provide access to spawn child (#18576)

# Why

Fixes ENG-7545

This proposal PR changes the API of the (node) package managers, with
the goal of:
- Having the right API options to install/remove packages to
`dependencies`/`devDependencies`/global deps
- Having access to the actual `spawnAsync` child, to pipe logs into
different systems (for example in EAS build)
- Allowing us to fix a couple of annoying DX issues (see follow up PRs)

> This is further outlined in the Package Manager API proposal.

Before merging this one, we need to merge these other PRs to not-break
`main`. Any feedback on the proposal is welcome, especially while in
draft.
- https://github.com/expo/expo/pull/19343
- https://github.com/expo/expo/pull/19344

# How

See Package Manager API proposal.

# Test Plan

> These changes are backward incompatible and require a new version
update.

This change also allowed us to implement the following fixes (all
stacked PRs):
- https://github.com/expo/expo/pull/19343
- https://github.com/expo/expo/pull/19344
- https://github.com/expo/expo/pull/19342
- https://github.com/expo/expo/pull/19340
- https://github.com/expo/expo/pull/19341
- https://github.com/expo/expo/pull/19764
- https://github.com/expo/expo/pull/19835
- https://github.com/expo/expo/pull/21189

# Checklist

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Please check the appropriate items below if they apply to your diff.
This is required for changes to Expo modules.
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- [x] Documentation is up to date to reflect these changes (eg:
https://docs.expo.dev and README.md).
- [ ] Conforms with the [Documentation Writing Style
Guide](https://github.com/expo/expo/blob/main/guides/Expo%20Documentation%20Writing%20Style%20Guide.md)
- [ ] This diff will work correctly for `expo prebuild` & EAS Build (eg:
updated a module plugin).

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