What does the toggle Device Management on iPhone System Services do?

This is used for the Apple Mobile Device Management (MDM) feature that IT administrators take advantage of to securely and wirelessly configure Apple devices. If you’re not using your device in a business environment as part of the MDM feature, you can safely turn it off. It should already be off, if you not in a corporate environment, and your iPhone is not managed by an office IT department.

Nobody can sign in to your iPhone remotely in any way. VPNs don't work that way either. VPNs connect a device to a secure network or proxy. They do not allow remote connections to the iPhone.

InOverMyHeadrn wrote:

Thank you, I am starting to feel better now after all the chaos that happened awhile back.

I wish there was a notification to show any paired past/current devices and who is connected to your wifi, bluetooth, & hotspot.

For a list of connected devices to your WiFi check your router's administration page. Consult your router's documentation and user guided for steps to access age administration page. All routers list connected devices in some way.

For Bluetooth, any connected devices to your iPhone should appear in the Bluetooth page in the Settings App.

For Hotspot, yes this is a sorely missed feature, but unless its turned on and you see a green pill shape over the clock at the top left corner of the iPhone screen, nobody is connected to your personal hotspot.

Status icons and symbols on your iPhone - Apple Support

You're on a call or your iPhone is providing a Personal Hotspot,*