Update fastapi requirement from ==0.110.* to ==0.111.* in /api

Updates the requirements on [fastapi](https://github.com/tiangolo/fastapi) to permit the latest version.
- [Release notes](https://github.com/tiangolo/fastapi/releases)
- [Commits](fastapi/fastapi@0.110.0...0.111.0)

---
updated-dependencies:
- dependency-name: fastapi
  dependency-type: direct:production
...

Signed-off-by: dependabot[bot] <support@github.com>

api/requirements.txt

@@ -1,3 +1,3 @@
-fastapi==0.110.*
+fastapi==0.111.*
 smart_open[s3]==7.0.*
 uvicorn[standard]==0.29.*