refactor: replace chrome storage api with wxt's storage api

[AntonVishal]

Implements: #527

This is the initial PR. I also have some ideas to implement storage.watch() from WXT in places where an explicit refresh is currently required for changes to reflect. This can be improved by adding some reactivity. I’ll be creating the next PR shortly.

Thanks @lirena00 for the heads-up.

And I would request @MaheshtheDev or @lirena00 to test it once more in their local before merging to main

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[lirena00]

Apologies for the delay in my response to work on this issue, I was caught up with some personal things.
I've reviewed the code, and it looks great and it does exactly what I intended. The only part missing is the .watch() functionality, which you've already noted you're working on.
Since @MaheshtheDev and @Dhravya are the maintainers, I'll defer to them for the final review and approval. Thanks for the work on this!