New infinite canvas feature is very cool. But when extending image dimensions, new area is transparent. Is there a plan for making background layer that would fill automatically those new areas?

No, not as such, because it is not needed. If you do not paint on the first layer, but add a paint layer and work on that, then if you press the extension area the extended first layer will be completely filled. Unless you paint on the first layer it is one pixel big that gets extended to the edges of the image -- so it will not take memory and it will be as big as the image anyway.

That only works if you create an image from custom image, other images won't do it.

Yes, that's right. But that is also the only case in which we have something like a background layer, I'd say.

Custom document must be the thing I missed. I was using 'Film templates', because in 'Custom document' panel 'create' button on my 1280x800 tablet is below screen area, and I'm unable to click it. I'm not sure if I should add this as bug - being unable to click 'create document' on small screens...

No... Screens that are that small are not officially supported. It actually works for me, even with a Plasma panel of 64 pixels high, but it's still not supported. But you might make it work by choosing a widget theme that has small widgets and a small font size.