I have Plan 2, I think editing online is exactly the same as Plan1? The drawing looks like this in Visio Online editor (attached)
The shapes are movable, you can copy and paste them. Just they look different from Visio (i.e. formatting is basically lost when you switch to edit)
Looks like they are converted into simple rectangles. I.e. when you open "View" you see the same thing as in Visio, but when you switch to "Edit In Browser" they become white rectangles.
Or maybe this is gradient fill not supported - not sure.
Personally, I've given up on Plan1. Not sure who might be the target audience of it. Maybe "there are no target customers but just targets" (c)
Now building completely on mxgraph (aka
https://diagrams.net) library (
https://github.com/jgraph/mxgraph).
Dear Visio Online, please come back when you grow up a bit and get support for apps and custom shapes

Honestly, mxgraph is not bad. And it's open source. In simple cases (like mine) when you don't need something fancy, it's good enough.
Even now, it can probably do more than Plan1. I was integrating it into SharePoint basically (SPFx), and now it might look even better than Visio

And remember, full source code available, and no iframes. Means, any shapes and any behaviors can be modified . Since basically it's all defined in (javascript) code.
Unfortunately it's more "like linux" - you can change everything and you will change everything.