Remove mini-oxygen dependency

[frandiox]

I forgot to remove mini-oxygen from the CLI's direct dependencies in #1891 (it's now a peer dep) . Also adding some minor cleanup to this PR.

[github-actions]

We detected some changes in packages/*/package.json or packages/*/src, and there are no updates in the .changeset.
If the changes are user-facing and should cause a version bump, run npm run changeset add to track your changes and include them in the next release CHANGELOG.
If you are making simple updates to examples or documentation, you do not need to add a changeset.

[shopify]

Oxygen deployed a preview of your fd-mini-oxygen-dep branch. Details:

Storefront	Status	Preview link	Deployment details	Last update (UTC)
subscriptions	✅ Successful (Logs)	Preview deployment	Inspect deployment	April 1, 2024 2:32 PM
third-party-queries-caching	✅ Successful (Logs)	Preview deployment	Inspect deployment	April 1, 2024 2:32 PM
custom-cart-method	✅ Successful (Logs)	Preview deployment	Inspect deployment	April 1, 2024 2:32 PM
vite	✅ Successful (Logs)	Preview deployment	Inspect deployment	April 1, 2024 2:32 PM
skeleton	✅ Successful (Logs)	Preview deployment	Inspect deployment	April 1, 2024 2:32 PM
optimistic-cart-ui	✅ Successful (Logs)	Preview deployment	Inspect deployment	April 1, 2024 2:32 PM

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