If WiFi worked before, there’s no reason it won’t work with a new ISP. It may be that the router provided by the ISP is crappier than your prior one, just buy your own router or AP

CTs would be the easiest option for longer term monitoring. Installation is non-invasive (to the wiring), and you can either buy a power monitoring system or design one yourself.

For something portable and non-permanent, a current clamp can be used to monitor a single device.

For a quick check, you could use a kill-a-watt