[eas-cli] Use production mode for Expo Updates commands

[ramonclaudio]

Stacked on #4180.

Why

EAS CLI can use an existing NODE_ENV when it resolves the runtime version or syncs Expo Updates config, which can make it load different env files for the same build. EAS CLI can also pass dotenv values loaded by a parent process to Expo Updates, which can make Expo Updates reuse values from a different mode.

How

I updated the Expo Updates commands to use production mode for runtime version resolution and Android and iOS config sync, and kept the original EAS CLI env unchanged. EAS CLI still supports Node 20.0.0, but @expo/env v2.5.0 requires Node 20.12.0, so I added the inherited dotenv cleanup locally for now.

Test Plan

Tests and package checks pass.

[linear-code]

DVT-119

[codecov]

Codecov Report

❌ Patch coverage is 88.00000% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 63.88%. Comparing base (df98b5f) to head (743749d).

Files with missing lines	Patch %	Lines
packages/eas-cli/src/utils/originalEnv.ts	85.72%	3 Missing ⚠️

Additional details and impacted files

@@                                Coverage Diff                                @@
##           @ramonclaudio/dvt-119-eas-config-mode-handoff    #4229      +/-   ##
=================================================================================
+ Coverage                                          63.86%   63.88%   +0.03%     
=================================================================================
  Files                                               1032     1033       +1     
  Lines                                              47511    47535      +24     
  Branches                                            9993     9999       +6     
=================================================================================
+ Hits                                               30338    30365      +27     
+ Misses                                             17072    17069       -3     
  Partials                                             101      101              

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[github-actions]

Subscribed to pull request

File Patterns	Mentions
packages/eas-cli/**	@douglowder
packages/eas-cli/src/update/**	@wschurman, @quinlanj

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[github-actions]

✅ Thank you for adding the changelog entry!

[ramonclaudio]

@expo-bot verify