Use auth code flow

[byronkarlen]

Why

Browser-based login should get a code and then exchange that code for a session_secret.

How

Used new auth flow provided by website/www. Uses state, code_challenge and code_verifier like OAuth 2.1.

Test Plan

Tested locally against expo.test with https://github.com/expo/universe/pull/24960
Made sure:

• works when user already logged in and selects existing account
• works when user already logged in and wants to log into another account
• works when user not already logged in
• the new flow is used
• errors with token exchange would be handled properly

Tested against expo.dev as well. Tried to test SSO but was hard since our stub-idp doesn't save state/users.

[codecov]

Codecov Report

❌ Patch coverage is 10.81081% with 33 lines in your changes missing coverage. Please review.
✅ Project coverage is 52.26%. Comparing base (13a6356) to head (4b6aafd).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
...es/eas-cli/src/user/expoBrowserAuthFlowLauncher.ts	10.82%	33 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3398      +/-   ##
==========================================
- Coverage   52.30%   52.26%   -0.03%     
==========================================
  Files         804      804              
  Lines       33421    33450      +29     
  Branches     6972     6975       +3     
==========================================
+ Hits        17478    17480       +2     
- Misses      14555    15885    +1330     
+ Partials     1388       85    -1303     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.

[github-actions]

Subscribed to pull request

File Patterns	Mentions
**/*	@douglowder

Generated by CodeMention

[tchayen]

XXXX?

[byronkarlen]

Whoops thank you! (geez claude)

[github-actions]

✅ Thank you for adding the changelog entry!