fix: dev ui url works in sub-apps

[racinmat]

Fixes #2072.
Blocked by #2556, it depends on it because of the base_url.
Supersedes #2254 because that did not get requested for review and adk-bot was not triggered there for some reason.
I didn't figure out any better way to do this. Basically we need to have a way how to provide a custom URL to the assets/config/runtime-config.json. I have tested with my project that it works well.

testing plan

I have added test that demonstrates the functionality in a sub-app.

I ran the relevant tests to my code and here are the results, everything passes.

 pytest ./tests/unittests/cli/test_fast_api.py   
======================================================================================================================= test session starts =======================================================================================================================
platform win32 -- Python 3.12.8, pytest-8.4.1, pluggy-1.6.0
rootdir: C:\Projects\others\adk-python
configfile: pyproject.toml
plugins: anyio-4.9.0, langsmith-0.3.45, asyncio-1.1.0, mock-3.14.1, xdist-3.8.0
asyncio: mode=Mode.AUTO, asyncio_default_fixture_loop_scope=function, asyncio_default_test_loop_scope=function
collected 36 items                                                                                                                                                                                                                                                 

tests\unittests\cli\test_fast_api.py ....................................                                                                                                                                                                                    [100%]

[racinmat]

@wyf7107 see how this PR is fixing the issues in the code, #2072 (comment)
and here the tests pass, you can verify it by running such test without the fix from my PR. It will fail.