Link field rendering as entity:node/2 instead of just /node/2

@imrodmartin in your example you return URI, so it does.
LinkItem(https://api.drupal.org/api/drupal/core%21modules%21link%21src%21Plugin%2...) has three properties: uri, title, options, so you can access them, you can as well render field using [block_content:field_button_link].
If you want go get url only, I think you should familiarize with this issue: https://www.drupal.org/project/token/issues/3112449 ✨ Token for link field URL Needs work
Anyway, it does not seem like the module issue.