No function displays after deploying self-hosted Python MCP project to Flex Consumption function app

[v-ruizh]

OS: Win 11 x64
Build Version: 20260513.1

Repro Steps:

1. Create a new self-hosted MCP server project with Python language.
2. Create a python Flex Consumption function app.
3. Deploy the project to the function app.
4. Check whether there is a function in the above function app.

Expect:
There is a function in the function app.

Actual:
No function displays in the python Flex Consumption function app.

More Info:

1. This issue does not reproduce for self-hosted C#/TypeScript MCP project.
   
2. This issue also reproduces for Python project created using "MCP trigger" template.

[nturinski]

Is this a regression? It used to work, right?

[v-ruizh]

Is this a regression? It used to work, right?

Conclusion: Not a regression.
Although the prior behavior is not fully certain, validation against previously released builds today confirms that this issue already existed, so it is not a regression.
The issue has been reproducible since v1.20.0, when self-hosted MCP server support was introduced.

Additionally:
A Python MCP trigger project alone does not reproduce this issue.
However, if a Function App has previously deployed a self-hosted MCP project, then deploying a Python MCP trigger project afterward results in no functions being shown in the Function App.