fix: Remove stateless "non-controllers" from background engine state

[MajorLift]

Description

Related issues

• Branches from https://github.com/MetaMask/metamask-mobile/pull/10441
• Implements https://github.com/MetaMask/core/issues/4444

Manual testing steps

1. Go to this page...

Screenshots/Recordings

Before

After

Pre-merge author checklist

• [ ] I’ve followed MetaMask Contributor Docs and MetaMask Mobile Coding Standards.
• [ ] I've completed the PR template to the best of my ability
• [ ] I’ve included tests if applicable
• [ ] I’ve documented my code using JSDoc format if applicable
• [ ] I’ve applied the right labels on the PR (see labeling guidelines). Not required for external contributors.

Pre-merge reviewer checklist

• [ ] I've manually tested the PR (e.g. pull and build branch, run the app, test code being changed).
• [ ] I confirm that this PR addresses all acceptance criteria described in the ticket it closes and includes the necessary testing evidence such as recordings and or screenshots.

[github-actions[bot]]

CLA Signature Action: All authors have signed the CLA. You may need to manually re-run the blocking PR check if it doesn't pass in a few minutes.

[socket-security[bot]]

New and removed dependencies detected. Learn more about Socket for GitHub ↗︎

Package	New capabilities	Transitives	Size	Publisher
npm/@metamask-previews/composable-controller@9.0.1-preview-335c4644	None	0	69.8 kB	mcmire, metamaskbot

🚮 Removed packages: npm/@metamask/composable-controller@9.0.0

View full report↗︎

[github-actions[bot]]

Bitrise

❌❌❌ pr_smoke_e2e_pipeline failed on Bitrise! ❌❌❌

Commit hash: 85c17e1f7aa6229644e5d72bf743d7d3c0fc57f9 Build link: https://app.bitrise.io/app/be69d4368ee7e86d/pipelines/f442d0cb-1b62-416c-9928-135dee1cba90

[!NOTE]

• You can kick off another pr_smoke_e2e_pipeline on Bitrise by removing and re-applying the Run Smoke E2E label on the pull request

[!TIP]

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[sonarcloud[bot]]

Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud