chore(2916): refactor stream handler for phishing warning and legacy stream

[DDDDDanica]

Description

As part of https://github.com/MetaMask/MetaMask-planning/issues/2916, it is cleaner to extract the stream out of contentscript file and re-use the logic of phishing stream before implement a new stream.

Related issues

Fixes: https://github.com/MetaMask/MetaMask-planning/issues/2916

Manual testing steps

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Screenshots/Recordings

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After

Pre-merge author checklist

• [ ] I've followed MetaMask Contributor Docs and MetaMask Extension 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.