What's the correct way to introduce custom frontend element and capability to Shopify storefront?

[Peterpot]

Hi, I want to add a custom button to a customer-facing e-commerce store that uses Shopify in the background to interact with Shopify API. Initially I thought I need to create a Shopify app for this purpose but I later discovered that a Shopify app is either embedded into the Shopify Admin dashboard or it's its own website, both of which are not what I want to do.

On the other hand, theme extension is able to add custom components to customer-facing online store website but it's using liquid instead of Shopify polaris and I don't think there is a way to interact with Shopify API. I read some tutorials on how Shopify uses OAuth and App Bridge to acquire an session jwt token to authenticate subsequent requests to Shopify app backend, but that doesn't seem to be applicable with theme extension.

So what is the correct way to achieve what I want to do, ie injecting a new frontend component in a customer-facing Shopify storefront that can interact with Shopify API and be designed with Polaris?

Thanks!