Package upgrade results in non-working Swagger document

**Describe the issue**
This issue possibly further clarifies what is happening in #596 and #594. The whole Swagger document does not render and `/api/swagger/ui` will not return a page.

**To Reproduce**
Steps to reproduce the behavior:
1. Follow all the steps as cited in [enable-open-api-endpoints-in-proc.md](https://github.com/Azure/azure-functions-openapi-extension/blob/main/docs/enable-open-api-endpoints-in-proc.md).
2. Now either having `Microsoft.Azure.WebJobs.Extensions.OpenApi` at version 1.5.x or having `Microsoft.Azure.WebJobs.Extensions.Storage` at version 5.1.3 (together with `Microsoft.Azure.WebJobs.Extensions.OpenApi` at 1.4.x) breaks the rendering of the Swagger document

**Expected behavior**
I expected that the swagger document would render, after doing a package upgrade.

**Screenshots**
-

**Environment (please complete the following information, if applicable):**
- OS: Windows 11 Pro 64-bit (10.0, Build 22621)
- Browser Firefox
- Version 116.0

Follow docs/enable-open-api-endpoints-in-proc.md to reproduce the failure with Microsoft.Azure.WebJobs.Extensions.OpenApi 1.5.x and with Storage 5.1.3 plus OpenApi 1.4.x. Compare the behavior with issues #596 and #594, then verify that the Swagger document renders and /api/swagger/ui returns a page after the package upgrade.

Written by the indexing model from the issue text.