[eas-cli] Fix invalid json for eas update with --json flag

[Mookiies]

@expo/fingerprint spawns subprocesses concurrently (autolinking, react-native config, ExpoConfigLoader) that can write to stdout, corrupting the parent process's output when --json is in use. The silent option exists specifically to suppress this, but was never set. The function is already named WithoutLogging so this is the correct default regardless of --json.

Why

We get this output often when running eas update with --json and --emit-metadata. The actual json conflict changes and flakes across update runs.

Executing eas update --branch staging --message "message" --private-key-path ~/keys/private-key.pem --clear-cache --emit-metadata --json --non-interactive
...
- Computing project fingerprints
✖ Failed to compute project fingerprints
⏩ To skip this step, set the environment variable: EAS_SKIP_AUTO_FINGERPRINT=1
Expected ':' after property name in JSON at position 2048
    Error: update command failed.

Exited with code exit status 1

ℹ 25 iOS assets, 25 Android assets (maximum: 2000 total per update). Learn more about asset limits: https://expo.fyi/eas-update-asset-limits
- Computing project fingerprints
✖ Failed to compute project fingerprints
⏩ To skip this step, set the environment variable: EAS_SKIP_AUTO_FINGERPRINT=1
Unexpected token 'R', ..."       "D"Release",
"... is not valid JSON
    Error: update command failed.

Wha'ts going on

1. `--json` monkey-patches `process.stdout`

eas-cli/src/utils/json.ts#L11-L12 — when `--json` is passed, eas-cli redirects `process.stdout.write → process.stderr.write` so progress logs don't pollute the final JSON output.

2. `@expo/fingerprint` spawns 5–6 subprocesses concurrently

@expo/fingerprint/src/sourcer/Sourcer.ts#L44-L79 — fingerprinting runs `getExpoAutolinkingAndroid`, `getExpoAutolinkingIos`, `getCoreAutolinkingFromExpoAndroid`, `getCoreAutolinkingFromExpoIos`, `getCoreAutolinkingFromRncCli`, and `getExpoConfig` all via `Promise.all()`. Each spawns a separate OS process.

3. Subprocess stdout is not subject to the in-process redirect

These are separate OS processes — the `process.stdout.write` monkey-patch in the parent has no effect on them. Any stray `console.log` from those subprocesses gets captured and `JSON.parse()`d by the parent.

4. There is a known IPC fallback that writes directly to stdout

@expo/fingerprint/src/ExpoConfigLoader.ts#L43-L46 — if `process.send` (IPC) is unavailable, `ExpoConfigLoader` falls back to `console.log(result)`, writing a multi-KB JSON blob directly to stdout, which then contaminates the parent's JSON stream.

5. The fix exists in `@expo/fingerprint` but eas-cli never uses it

eas-cli/src/fingerprint/cli.ts#L89-L108 — `@expo/fingerprint` has a `silent: true` option specifically to suppress subprocess stdout pollution in JSON contexts, but `createFingerprintWithoutLoggingAsync` never sets it.

How

Suppress output from fingerprinting by suppressing output

Test Plan

Repeatedly run eas update --branch staging --message "message" --emit-metadata --json --non-interactive and watch for intermitent failures on fingerprinting fail due to invalid JSON. If it always works and doesn't flake good to go.

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[douglowder]

Looks good, please add a changelog entry in CHANGELOG.md

[Mookiies]

@douglowder Rebased onto latest main to avoid conflicts in changelog and added new entry