### Apache Airflow version

2.2.2 (latest released)

### What happened

Warnings `{providers_manager.py:156} WARNING - Exception when importing 'airflow.providers.google.leveldb.hooks.leveldb.LevelDBHook' from 'apache-airflow-providers-google' package: No module named 'plyvel'` appear in `wait-for-airflow-migrations` init containers and during webserver pod start.

### What you expected to happen

No such warnings, they were not present in 2.1.3 version.

### How to reproduce

Install Airflow using airflow helm chart with 2.2.2 airflow docker image and check `wait-for-airflow-migrations` init containers logs. Warnings can also be seen in webserver container.

### Operating System

Debian “buster”

### Versions of Apache Airflow Providers

Providers that come with the official Airflow docker image.

### Deployment

Official Apache Airflow Helm Chart

### Deployment details

_No response_

### Anything else

Looking at commit history, isn't this supposed to be a debug level log as per https://github.com/apache/airflow/commit/2f32df7b711cf63d18efd5e0023b22a79040cc86#diff-c56df299b30e60d690494057a4e8721d36406c0cca266961ff2ae6504993c8cb ?

Seems like this logic was changed in https://github.com/apache/airflow/commit/29aab6434ffe0fb8c83b6fd6c9e44310966d496a#diff-c56df299b30e60d690494057a4e8721d36406c0cca266961ff2ae6504993c8cbL288 since `_sanity_check`  doesn't handle `ImportError`s as debug messages . Should these warnings be ignored for now?

### Are you willing to submit PR?

- [X] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

airflow/providers_manager.py
if cls._instance is None:
            cls._instance = super().__new__(cls)
        return cls._instance
    def __init__(self):
        """Initializes the manager."""
        super().__init__()
        self._initialized_cache: Dict[str, bool] = {}
        
        self._provider_dict: Dict[str, ProviderInfo] = {}
        
        self._hooks_dict: Dict[str, HookInfo] = {}
        self._taskflow_decorators: Dict[str, Callable] = LazyDictWithCache()
        
        self._hook_provider_dict: Dict[str, HookClassProvider] = {}
        
        self._hooks_lazy_dict: LazyDictWithCache[str, Union[HookInfo, Callable]] = LazyDictWithCache()
        
        self._connection_form_widgets: Dict[str, ConnectionFormWidgetInfo] = {}
        
        self._field_behaviours: Dict[str, Dict] = {}
        self._extra_link_class_name_set: Set[str] = set()
        self._logging_class_name_set: Set[str] = set()
        self._secrets_backend_class_name_set: Set[str] = set()
        self._api_auth_backend_module_names: Set[str] = set()
        self._provider_schema_validator = _create_provider_info_schema_validator()
        self._customized_form_fields_schema_validator = (
            _create_customized_form_field_behaviours_schema_validator()
        )
    @provider_info_cache("list")
    def initialize_providers_list(self):