chore!: Sets up google_adk for top level logger namespace. Removes --log_to_tmp option in adk web and adk api_server for the same reason.

Context: google-auth commit [1] broke adk log, because it disables the top level logger named "google", which is also adk's top level logger. We establish a separate top level logger with a different name `google_adk` to prevent this in the future.

This commit only changes google_llm.py. All other files will be changed in later commits.

[1] 77ad53eb00 (diff-e386c2b2c39b4d746c1e257f503acecbde49b1746b1a34f53b57083ed6094161)

PiperOrigin-RevId: 759872317

src/google/adk/cli/cli_tools_click.py

@@ -408,16 +408,6 @@ def cli_eval(
     default="INFO",
     help="Optional. Set the logging level",
 )
-@click.option(
-    "--log_to_tmp",
-    is_flag=True,
-    show_default=True,
-    default=False,
-    help=(
-        "Optional. Whether to log to system temp folder instead of console."
-        " This is useful for local debugging."
-    ),
-)
 @click.option(
     "--trace_to_cloud",
     is_flag=True,
@@ -439,7 +429,6 @@ def cli_eval(
 )
 def cli_web(
     agents_dir: str,
-    log_to_tmp: bool,
     session_db_url: str = "",
     log_level: str = "INFO",
     allow_origins: Optional[list[str]] = None,
@@ -457,10 +446,7 @@ def cli_web(
 
     adk web --session_db_url=[db_url] --port=[port] path/to/agents_dir
   """
-  if log_to_tmp:
-    logs.log_to_tmp_folder(getattr(logging, log_level.upper()))
-  else:
-    logs.log_to_stderr(getattr(logging, log_level.upper()))
+  logs.setup_adk_logger(getattr(logging, log_level.upper()))
 
   @asynccontextmanager
   async def _lifespan(app: FastAPI):
@@ -542,16 +528,6 @@ def cli_web(
     default="INFO",
     help="Optional. Set the logging level",
 )
-@click.option(
-    "--log_to_tmp",
-    is_flag=True,
-    show_default=True,
-    default=False,
-    help=(
-        "Optional. Whether to log to system temp folder instead of console."
-        " This is useful for local debugging."
-    ),
-)
 @click.option(
     "--trace_to_cloud",
     is_flag=True,
@@ -575,7 +551,6 @@ def cli_web(
 )
 def cli_api_server(
     agents_dir: str,
-    log_to_tmp: bool,
     session_db_url: str = "",
     log_level: str = "INFO",
     allow_origins: Optional[list[str]] = None,
@@ -593,10 +568,7 @@ def cli_api_server(
 
     adk api_server --session_db_url=[db_url] --port=[port] path/to/agents_dir
   """
-  if log_to_tmp:
-    logs.log_to_tmp_folder(getattr(logging, log_level.upper()))
-  else:
-    logs.log_to_stderr(getattr(logging, log_level.upper()))
+  logs.setup_adk_logger(getattr(logging, log_level.upper()))
 
   config = uvicorn.Config(
       get_fast_api_app(