Yes. Sony’s Imaging Edge Mobile app replaced PlayMemories Mobile for camera-to-phone transfers. It supports the same core functions, including wireless image transfer from compatible Sony cameras.

For your use case, the key point is that wireless transfer can be done directly between the camera and phone; it does not require using PlayMemories Online cloud storage. If you want to avoid the cloud, use the app’s direct transfer features rather than any online syncing service.

One community answer notes a 2 MiB limit for transferred images, but that appears to be an inference rather than a confirmed cloud requirement. The practical takeaway is: use Imaging Edge Mobile as the current Sony-supported option for wireless transfer, and avoid any cloud-upload features if privacy is your concern.