Fixes #2238.
Makes the logic changed by #2520 flexible and usable by agents defined in the same application.
Supersedes #2251 because that did not get requested for review and adk-bot was not triggered there for some reason.
This is more generic and allows you to set http or https as needed, which is crucial in larger ecosystems.
And it lets you nest the FastAPI into a subapp, because you can specify the base url including the path of the sub-app.

If the url parameter in agent card is empty string, it will be filled from the application. This lets you either hardcode the agent url or let it be defined from the code.

testing plan

The tests can be seen in the PR.
I removed the mock to actually exercise the A2A-related code which was just silently crashing until now.

Now, with this with, you can run

from pathlib import Path
import uvicorn
from fastapi import FastAPI
from google.adk.cli.fast_api import get_fast_api_app
app = FastAPI()
adk_app = get_fast_api_app(
    agents_dir=str((Path(__file__) / '..').absolute()),
    session_service_uri="sqlite:///:memory:",
    allow_origins=["*"],
    web=True,
    base_url="http://127.0.0.1:8081/adk",
)
app.mount("/adk", adk_app)
uvicorn.run(app, host="0.0.0.0", port=8081)

and the a2a agent will be exposed on the localhost. And if you will run the code in different environments, you can parameterize them now, and pass the URL e.g. from environment variable, which wasn't possible after merging #2520.