Continuing the work from #2915, we should add an option to the logging integration (https://docs.sentry.io/platforms/dart/integrations/logging/) that allows you to send logging logs as sentry logs.

We should decide if we want to enable this by default if enable_logs is true, or gate it behind another option/integration. We'll probably still want an option that controls what log levels get captured as logs as well.

Spec: https://develop.sentry.dev/sdk/telemetry/logs/#sdk-integrations