Migrate `StatsigIntegration` from `statsig` (legacy) to `statsig-python-core` pip package

### Problem Statement

The [StatsigIntegration](https://github.com/getsentry/sentry-python/blob/master/sentry_sdk/integrations/statsig.py) uses [`statsig`](https://pypi.org/project/statsig/) library underneath.

The old [`statsig`](https://pypi.org/project/statsig/) library is called as **legacy** in Statsig's [documentation](https://docs.statsig.com/server/pythonSDK)

It forces us to either:
- use the new (recommended) library but without Sentry integration
- use the old one with Sentry integration

### Solution Brainstorm

Documentation for the new one ([`statsig-python-core`](https://pypi.org/project/statsig-python-core/)) is [here](https://docs.statsig.com/server-core/python-core)

Start with sentry_sdk/integrations/statsig.py and compare its current legacy statsig usage with the statsig-python-core documentation linked in the issue. Trace the integration entry points and preserve Sentry integration while migrating the dependency; done means StatsigIntegration works with the recommended package rather than the legacy one.

Escrita pelo modelo de indexação a partir do texto da issue.