[chore] Switch to publishing with OIDC

[sjchmiela]

Why

https://exponent-internal.slack.com/archives/C017N0N99RA/p1769306804484099

How

Applied a few of the changes we've done to eas-build:

• expo/eas-build@784e37c
• expo/eas-build@ae9dbea
• expo/eas-build@ec824f1
• expo/eas-build@54ff4e9

Test Plan

Merge and try releasing a new version.

[github-actions]

Size Change: +7.53 kB (+0.01%)

Total Size: 53.2 MB

Filename	Size	Change
./packages/eas-cli/dist/eas-linux-x64.tar.gz	53.2 MB	+7.53 kB (+0.01%)

_{compressed-size-action}

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 49.67%. Comparing base (6eeb15b) to head (b225b62).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #3342   +/-   ##
=======================================
  Coverage   49.67%   49.67%           
=======================================
  Files         671      671           
  Lines       28018    28018           
  Branches     5802     5802           
=======================================
  Hits        13914    13914           
  Misses      12916    12916           
  Partials     1188     1188           

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[github-actions]

Subscribed to pull request

File Patterns	Mentions
**/*	@douglowder

Generated by CodeMention

[github-actions]

⏩ The changelog entry check has been skipped since the "no changelog" label is present.

[kadikraman]

I think we need to set the provenance env var here? https://docs.npmjs.com/generating-provenance-statements#using-third-party-package-publishing-tools

As in:

        env:
          NPM_CONFIG_PROVENANCE: true

[sjchmiela]

I didn't need to do it for eas-build so not sure…

[kadikraman]

I used it for the styleguide but I never tried publishing without so I don't know for sure! Maybe lerna handles it under the hood. Can try without and add it if publish fails 🤷‍♀️