In order to extend this application to serve as a media library for your home, you would need to determine what media types you want to serve and where they are located. 

Assuming all your files are located in a directory called `media` and that you are okay relying on the web browser's default display for your files, the following code would allow your files to be accessible from your local network:

```python
from fastapi import FastAPI
from fastapi.staticfiles import StaticFiles

app = FastAPI()

app.mount("/", StaticFiles(directory="media"), name="media")

```

This will only be accessible on your local network. You may need to configure firewall rules and port forwarding to make this accessible outside your home.
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