fix(package-manager): detect `bun` before `yarn` to allow `bun install --yarn` usage (#24360)

# Why

Some people value readable lock files, and unfortunately, `bun.lockb`
isn't readable. Bun has

fix(package-manager): detect `bun` before `yarn` to allow `bun install --yarn` usage (#24360)

# Why

Some people value readable lock files, and unfortunately, `bun.lockb`
isn't readable. Bun has a feature for this, where it exports both a
`bun.lockb` and `yarn.lock` (based on `bun.lockb`).

For that reason, we should resolve `bun` before `yarn`. If people use
`bun install --yarn`, we always resolve to `yarn`.

# How

- Move `bun` detection before `yarn`.

# Test Plan

- `$ bun create expo ./test -t tabs`
- `$ cd ./test`
- `$ bun install --yarn`
- `$ bun expo install`
- _Should use `bun` to install_

# Checklist

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feat: detect Bun package manager (#24168)

# Why

Adds Bun as a recognized package manager

Sister PR: https://github.com/expo/expo-cli/pull/4752

# How

Added `@expo/package-manager`

# Te

feat: detect Bun package manager (#24168)

# Why

Adds Bun as a recognized package manager

Sister PR: https://github.com/expo/expo-cli/pull/4752

# How

Added `@expo/package-manager`

# Test Plan

Added `BunPackageManager-test.ts` and added Bun tests to
`nodeManagers-test.ts`.

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tests! If possible, please also provide terminal output and/or
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# Checklist

---------

Co-authored-by: Evan Bacon <[email protected]>
Co-authored-by: Expo Bot <[email protected]>

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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

<!--
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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