Move logic for handling partial api responses and errors to vets-api

[JRRoof]

Description

Move any existing logic for handling partial api responses and errors in the appointments web application to the vets-api layer.

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Development Checklist

• Identify and document logic in the appointments web application
• Move existing logic to the vets-api layer
• Add additional parameters as needed
• Verify vets-api responses matches existing logic in appointments web application

Design Assets

• N/A

Developer Reference

N/A

Definition of Done

• All tasks criteria are met
• Technical Documentation is updated (must confirm if needed/or remove)

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