## Bug description

personal_api_key.last_updated_at is updated every request with API keys.

This is one of the most time-consuming queries we do against postgres: https://metabase.posthog.net/question/344-most-time-consuming-postgres-queries


## Environment

- [x] PostHog Cloud
- [ ] self-hosted PostHog (ClickHouse-based), version/commit: _please provide_
- [ ] self-hosted PostHog (Postgres-based, legacy), version/commit: _please provide_

## Additional context

There's a half-hearted attempt at fixing this over at https://github.com/PostHog/posthog/pull/10383, but this was shot down due to UX concerns.

#### *Thank you* for your bug report – we love squashing them!

posthog/auth.py
"""A way of authenticating with personal API keys.
    Only the first key candidate found in the request is tried, and the order is:
    1. Request Authorization header of type Bearer.
    2. Request body.
    3. Request query string.
    """
    keyword = "Bearer"
    @classmethod
    def find_key_with_source(
        cls,
        request: Union[HttpRequest, Request],
        request_data: Optional[Dict[str, Any]] = None,
        extra_data: Optional[Dict[str, Any]] = None,
    ) -> Optional[Tuple[str, str]]:
        """Try to find personal API key in request and return it along with where it was found."""
        if "HTTP_AUTHORIZATION" in request.META:
            authorization_match = re.match(fr"^{cls.keyword}\s+(\S.+)$", request.META["HTTP_AUTHORIZATION"])
            if authorization_match:
                return authorization_match.group(1).strip(), "Authorization header"
        data = request.data if request_data is None and isinstance(request, Request) else request_data
        if data and "personal_api_key" in data:
            return data["personal_api_key"], "body"
        if "personal_api_key" in request.GET:
            return request.GET["personal_api_key"], "query string"
        if extra_data and "personal_api_key" in extra_data:
            
            return extra_data["personal_api_key"], "query string data"
        return None
    @classmethod
    def find_key(