Shopify has recently announced the following:
"As of January 1, 2023 stores on Starter and Basic plans (globally), will no longer be able to request access to the Carrier Service API. The option to request access by transitioning to annual billing or by paying an additional monthly fee for these plan types will be removed.
Stores on Advanced and Shopify Plus plans will continue to have access to Carrier Service API. Stores on Shopify plans can continue to request access by contacting Shopify Support. Stores on Starter or Basic plans that were previously granted access are not impacted by this change.
Learn more about CarrierService access requirements on Shopify.dev."
In short, this means you will need a Shopify subscription plan higher than Basic, in order to use Webshipper shipping rates in checkout.
The cheapest Shopify Subscription plan that is usable with Webshipper is therefore the Shopify plan.
Please be aware, if you (or Shopify) make any changes to your current subscription plan, you will most likely need to re-enable Shopify's Third party Calculated rates again.
And should you do this, we cannot guarantee that your current integration will continue to function without having a higher subscription plan with Shopify.
If you have any questions, please contact Shopify support directly. Thank you in advance.