I thought my first thoughts might be useful.
It comes in a well presented quality packing which is a good start. About as innovative as the camera itself - diagonal opening box. So it starts off well. There were an assortment of plug ends for the adapter - US, UK and EU general but no AU plug which is a bit odd as the Chinese plug is none other than an AU plug that fits upside down in the socket. Maybe this was not made for the Chinese market? In any case the EU plug fitted into my "universal adapter" easily enough but the US and UK plugs were not that interested - but no matter it charged the batteries ok.
The batteries were a surprise - they were much larger physically than I had expected.
Compared to the standard Panasonic BLH7E for the GM series cameras

The battery takes up a large slab of the body space:

Compared to the GM series there is not a lot of difference in it:

w x d x h (mm) my measurements
Z E1: 75.5 x 27.5 x 56.0 But the mount tube protrudes a further 21.0 mm
GM5: 98.5 x 23.5 x 59.5 The mount tube only protrudes a further 6.8mm
Therefore the displaced volume of the Z E1 is not that much less than even a GM5, but the shape is probably friendlier for a gimbal mount. And chunkier for those that wish to use it by gripping it.
In use it was quite friendly once I started to get used to the button controls. The firmware upgraded to v0.30 easily. I could set up date and move around the menu system within a short learning process. It always defaults to video recording at startup but a click on the toggle mode dial swaps to stills instantly. A nuisance in not remembering "last used". Focus seems adequate and the DR of actual captures looks better on the finished product than it does on the screen.
I finally fund that playback was a long press on the mode button.
Not sure what was going on but 6 captures produced 83 images - I think that as there is not a lot of feedback on the shutter button a short press and release will be enough. Unless there is an issue with button bounce as I had it set for single capture and not burst.
I does start to get noticeably hot in use, not enough top bother me in my little stills and minor video test but it would obviously get hotter if used extensively for video.
There is no mount for a wrist strap so I have attached one via the (seems like a plastic thread) tripod mount.
So far I have just used the camera with the Panasonic 12-32 kit lens. Seems to work well - I am probably a little more unusual as I am more interested in it as a stills camera.
It certainly only shares a size category with the GM series - it is such a different experience as to have a niche of its own - once I figure out exactly what it is
Am I happy I bought one - yes of course and I will get some fun trying out more lenses on it. This is day one and I have hardly had a real chance to explore beyond figuring out how to set it up.
A neat touch is that when you press the menu button a row of the essential controls are presented as icons. When selected by the function button they then retire to the foot of the screen but the selected function remains highlighted in red and and can be adjusted by the adjustment keys. Somehow this feels quite natural for a little camera that has no wheels, 4-way controller or touch screen. Somehow a quite intuitive interface has been thought out for such a few basic button controls. For someone who gets quite spitty over poor user interfaces the control structure is basic but well thought out. I have not minded it so far on my first day's wrestle.