I am looking for a Zigbee Outlet the measures power also, but can handle the power surge of a dryer. I have a few Samsung Smartthings Outlets, but they will pop randomly when the dryer starts and have to be reset with their button.
Is your dryer 120 or 240? If the former, the ZEN15 above should work. If it's more, Aeon has a heavy-duty meter (not a plug; I don't know of any for 240 in the US) I've never used but maybe someone here has...
Again it's not Zigbee, it's Zwave but I have a Zooz Power Strip running an Upright Freezer, and a Refrigerator both side by side on one power strip and each hit upwards of 800 watts on start ups, should work for your dryer and you could add your washer as well. I have Fibaro wall plugs (zwave also) on a microwave that has 1500-1600 running watts.
The ZEN15 is specifically marketed as "heavy duty" for applications like these; I can't find specs for the ST outlet (wish I knew if it was OK to use for small motors Iike fans; I might risk it anyway) but most wouldn't fare well with any dryer, so I suspect that's the problem. The ZEN15 should be fine, and I'm sure Zooz support would be helpful (they're great!) if you have problems.