Hi folks,
From looking into this deprecation from last year, it doesn’t appear that there’s a replacement for getting a specific countries tax with the Shopify API: Deprecation Notice: Country and Province Endpoints in Admin REST API — Shopify developer changelog
One workaround could be to store the tax rate as a metafield that can be accessed via the API, but to get the rate when creating the metafield, you’d need to manually access this value.