[Typescript Conversion: Level 1]: Convert app/scripts/background.js to typescript

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## **Description**

Convert `app/scripts/background.js` from JavaScript to TypeScript as part of the TS migration initiative.

## **Scenario (for user stories only)**

_(Not applicable)_

## **Design (for user stories only)**

_(Not applicable)_

## **Technical Details (for technical tasks only)**

- Convert this file to TypeScript.
- Migration Level: **1**
- Dependencies:
- app/scripts/first-time-state.js
- app/scripts/lib/createStreamSink.js
- app/scripts/lib/ens-ipfs/setup.js
- app/scripts/lib/get-first-preferred-lang-code.js
- app/scripts/lib/getObjStructure.js
- app/scripts/lib/migrator/index.js
- app/scripts/lib/notification-manager.js
- app/scripts/lib/util.ts
- app/scripts/metamask-controller.js
- app/scripts/migrations/index.js
- app/scripts/platforms/extension.js
- shared/constants/app.ts
- shared/constants/metametrics.ts
- shared/modules/mv3.utils.js
- shared/modules/object.utils.js
- Dependents:
- None

## **[Threat Modeling Framework](https://github.com/adamshostack/4QuestionFrame) (for technical tasks only)**

- What are we working on? Convert file to TypeScript.
- What can go wrong? Type errors, integration mismatches, missing types.
- What are we going to do about it? Write types carefully and test thoroughly.
- Did we do a good job? _(To be evaluated)_

## **Acceptance Criteria**

- File is fully converted to TypeScript.
- Tests pass.
- File adheres to linting rules.
- Functionality remains unchanged.

## **Stakeholder Review (for MetaMask employees only)**

- [X] Engineering
- [ ] Design
- [ ] Product
- [ ] QA
- [ ] Security
- [ ] Legal
- [ ] Marketing
- [ ] Management
- [ ] Other

## **References**

- Parent issue: #31460

Start with app/scripts/background.js and read the listed dependencies to understand its interfaces before converting it. Run the relevant tests and lint checks; done means the file is fully converted to TypeScript, behavior is unchanged, and tests and linting pass.

Written by the indexing model from the issue text.