Support for synchronous auth flow with separate re-entry #1724

Description

I work on the Google ADK and we are adding support for PRM-based authentication. We would like to use the OAuthClientProvider reference library, but it is unfortunately incompatible with the existing ADK usage pattern.

Google ADK usage pattern

events = agent.run('call my tool')  # without auth
for event in events:
  # find auth request and handle it (e.g. open web url, etc.)

events = agent.run(/* auth response */)
for event in events:
  # get tool call result

Reference for exact details (https://google.github.io/adk-docs/tools-custom/authentication)

This pattern requires that the authorization request URL be surfaced to the caller and the initial flow be ended, only to be re-started again later once the authorization code is available. This is similar to how the MCP typescript reference library functions, while the python library requires a continuous flow mediated by async callbacks.

If support for this additional pattern is acceptable with the python SDK maintainers, I'm able to make a contribution, and would like to get consensus on one of the following designs:

1. Core implementation is refactored into the synchronous pattern, and the asynchronous pattern is maintained as a thin layer over this.
2. A single implementation is maintained and accepts a constructor param governing which pattern it should use.
3. A separate implementation is maintained for each pattern, re-using some core components of the library wherever possible.

Thanks!

References

No response