Refactor: Migrate from chrome.storage to wxt/storage for extension

[lirena00]

I suggest refactoring our storage layer to use WXT's built-in storage solution (wxt.storage) instead of the currently used chrome.storage.

WXT Storage Documentation: https://wxt.dev/storage.html

The current chrome.storage API is not ideal for cross-browser compatibility, which can create issues when targeting browsers like Firefox (because specifically speaking I need the extension on firefox as well, it's free to register over there unlike chrome webstore).

Benefits of Migrating to wxt.storage

• Cross-browser Compatibility: It automatically uses the correct storage API for the target browser.
• Typesafety: It's designed to work seamlessly with TypeScript.
• Built-in Migrations: It provides a clear API for handling storage migrations as the data schema evolves.
• Reactivity: It includes storage watchers (storage.watch()), which will help simplify state management and improve code maintainability.

I am willing to work on implementing this change. Given the scope, I wanted to raise this issue first to confirm if this is a direction you're interested in as it will also require rewrites. If you agree, you can assign this issue to me.

[linear[bot]]

ENG-342

[MaheshtheDev]

@lirena00 assigned to you. feel free to create PR