feat(logging): implement category-based logging (#1362)

# What does this PR do?

This commit introduces a new logging system that allows loggers to be
assigned
a category while retaining the logger name based on the file name. The
log
format includes both the logger name and the category, producing output
like:

```
INFO     2025-03-03 21:44:11,323 llama_stack.distribution.stack:103 [core]: Tool_groups: builtin::websearch served by
         tavily-search
```

Key features include:

- Category-based logging: Loggers can be assigned a category (e.g.,
  "core", "server") when programming. The logger can be loaded like
  this: `logger = get_logger(name=__name__, category="server")`
- Environment variable control: Log levels can be configured
per-category using the
  `LLAMA_STACK_LOGGING` environment variable. For example:
`LLAMA_STACK_LOGGING="server=DEBUG;core=debug"` enables DEBUG level for
the "server"
    and "core" categories.
- `LLAMA_STACK_LOGGING="all=debug"` sets DEBUG level globally for all
categories and
    third-party libraries.

This provides fine-grained control over logging levels while maintaining
a clean and
informative log format.

The formatter uses the rich library which provides nice colors better
stack traces like so:

```
ERROR    2025-03-03 21:49:37,124 asyncio:1758 [uncategorized]: unhandled exception during asyncio.run() shutdown
         task: <Task finished name='Task-16' coro=<handle_signal.<locals>.shutdown() done, defined at
         /Users/leseb/Documents/AI/llama-stack/llama_stack/distribution/server/server.py:146>
         exception=UnboundLocalError("local variable 'loop' referenced before assignment")>
         ╭────────────────────────────────────── Traceback (most recent call last) ───────────────────────────────────────╮
         │ /Users/leseb/Documents/AI/llama-stack/llama_stack/distribution/server/server.py:178 in shutdown                │
         │                                                                                                                │
         │   175 │   │   except asyncio.CancelledError:                                                                   │
         │   176 │   │   │   pass                                                                                         │
         │   177 │   │   finally:                                                                                         │
         │ ❱ 178 │   │   │   loop.stop()                                                                                  │
         │   179 │                                                                                                        │
         │   180 │   loop = asyncio.get_running_loop()                                                                    │
         │   181 │   loop.create_task(shutdown())                                                                         │
         ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
         UnboundLocalError: local variable 'loop' referenced before assignment
```

Co-authored-by: Ashwin Bharambe <@ashwinb>
Signed-off-by: Sébastien Han <seb@redhat.com>

[//]: # (If resolving an issue, uncomment and update the line below)
[//]: # (Closes #[issue-number])

## Test Plan

```
python -m llama_stack.distribution.server.server --yaml-config ./llama_stack/templates/ollama/run.yaml
INFO     2025-03-03 21:55:35,918 __main__:365 [server]: Using config file: llama_stack/templates/ollama/run.yaml           
INFO     2025-03-03 21:55:35,925 __main__:378 [server]: Run configuration:                                                 
INFO     2025-03-03 21:55:35,928 __main__:380 [server]: apis:                                                              
         - agents                                                     
``` 
[//]: # (## Documentation)

---------

Signed-off-by: Sébastien Han <seb@redhat.com>
Co-authored-by: Ashwin Bharambe <ashwin.bharambe@gmail.com>

llama_stack/providers/utils/inference/litellm_openai_mixin.py

@@ -8,7 +8,6 @@ from typing import AsyncGenerator, AsyncIterator, List, Optional, Union
 
 import litellm
 
-from llama_stack import logcat
 from llama_stack.apis.common.content_types import (
     InterleavedContent,
     InterleavedContentItem,
@@ -33,6 +32,7 @@ from llama_stack.apis.inference import (
 )
 from llama_stack.apis.models.models import Model
 from llama_stack.distribution.request_headers import NeedsRequestProviderData
+from llama_stack.log import get_logger
 from llama_stack.providers.utils.inference.model_registry import (
     ModelRegistryHelper,
 )
@@ -47,6 +47,8 @@ from llama_stack.providers.utils.inference.prompt_adapter import (
     interleaved_content_as_str,
 )
 
+logger = get_logger(name=__name__, category="inference")
+
 
 class LiteLLMOpenAIMixin(
     ModelRegistryHelper,
@@ -109,8 +111,7 @@ class LiteLLMOpenAIMixin(
         )
 
         params = await self._get_params(request)
-        logcat.debug("inference", f"params to litellm (openai compat): {params}")
-
+        logger.debug(f"params to litellm (openai compat): {params}")
         # unfortunately, we need to use synchronous litellm.completion here because litellm
         # caches various httpx.client objects in a non-eventloop aware manner
         response = litellm.completion(**params)