fix(app): classify existing web profiles for layout transition

[dleopold]

Issue for this PR

Fixes #38124

Partially addresses #37546 by restoring the web layout escape hatch. Workspace support in the new layout remains outside this PR.

Related context: #37012 requests retaining the legacy layout permanently; this PR does not change the existing sunset policy.

Type of change

• Bug fix
• New feature
• Refactor / code improvement
• Documentation

What does this PR do?

Existing web profiles never receive layoutTransitionEligible because eligibility is currently initialized only by desktop onboarding. As a result, the existing layout transition control is hidden on web.

This change classifies previously unclassified web profiles once persisted settings and launch state are ready:

• profiles with existing settings.v3 state or a recorded app version are eligible
• blank web profiles are explicitly ineligible
• the result is persisted in the existing settings field
• desktop eligibility remains unchanged
• the existing layout sunset remains unchanged

This keeps the original transition behavior: existing users get the temporary escape hatch, while blank profiles start on the new layout without the option to switch back.

How did you verify your code works?

• bun test src/context/settings.test.ts — 12 passed, 0 failed
• bun typecheck — passed
• bun run build — passed
• Manually tested the production preview:
  • blank web profile did not show the layout transition control
  • existing web state caused the control to appear
  • switching to the previous layout worked
  • the selected layout persisted after reload

Screenshots / recordings

The rendered control is unchanged; this PR only makes the existing control reachable for eligible web profiles.

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR

[github-actions]

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Please:

1. Open an issue describing the bug/feature (if one doesn't exist)
2. Add Fixes #<number> or Closes #<number> to this PR description

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[onelpawarai]

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