All entities are saying "No statistics found" & "This entity is no longer being recorded". What to do?

You can run that command from within the SSH & Web Terminal Add-On. Once you stop Core you lose all access to the Terminal as well as to the HA interface (including the File Editor and Nabu Casa), so you can’t restart it without physically power-cycling it.

You would first install and configure the Samba Share Add-On and make sure you can access the config folder from an external computer before stopping Core: the Samba shares are still accessible afterwards so you can rename the file.

If you don’t have physical access to the hardware I suggest using a power switch that can be accessed from the internet (Cloud) such as the Sonoff S31 WiFi or a Shelly Plug.

Edit: You could restart HA if it’s installed in a VM such as Proxmox from within the VM environment, assuming you have remote access to the VM server such as thru a VPN.