API calls fail on temp deployments in PRs

When creating a PR for a Static Web App on GitHub, my API calls all fail with "Backend call failure". This response is returned after several seconds, so this might be some kind of timeout behavior. The same app works fine locally and with the deployment from my main branch. I've had this behavior with both Node 12 and Node 16 APIs.

Steps to reproduce the behavior:
1. Create a PR for a GitHub repo containing a Static Web App. In my case, I am using https://github.com/kbarnes3/whos-there/
2. Wait for the CI pipeline to publish a staging site and go to it.
3. Observe that every API call fails with "Backend call failure" after a few seconds

My source and configuration files are all public here: https://github.com/kbarnes3/whos-there/. The production deployment is available at:
https://whos-there.kbarnes3.com/
https://ashy-bush-00c3f3c1e.azurestaticapps.net/

A staging deployment ([source PR](https://github.com/kbarnes3/whos-there/pull/111)) demonstrating this problem is here:
https://ashy-bush-00c3f3c1e-111.westus2.azurestaticapps.net/

**Expected behavior**
API calls on staging deployments should behave similarly as they do in production.