Update settings in A2A to be compatible with new settings v2

[sehoon38]

What happened?

Settings were upgraded to support more nested structure, and currently A2A settings do not respect this new structure and some of the settings will not read the new nested structure setting.

What did you expect to happen?

We'd like to make sure both old and new format is respected in A2A settings, for both backward compatibility and the new structure.

Client information

Client Information

Run gemini to enter the interactive CLI, then run the /about command.

> /about
# paste output here

Login information

No response

Anything else we need to know?

No response