So at 12”tall that would hold 10g. Taller that that might be a bit tippy, unless you could think of a way to anchor it (some kind of custom bracket, maybe).
One of my tanks is in a window - when it had a piece of textured but transparent yellow glass as a backdrop, I did run into excess algae (the glass looked awesome, though), but now with a black background behind it, it’s fine. Could depend on the window direction - mine is west facing. North might be less problematic.
Your scaping would only be one item deep - one plant, one rock, one stick, so the design would be an interesting challenge with a 2-dimensional effect. Having focal point fish like a betta might offset the simplicity. A large school of nano’s could work as well.
You could mount a shelf right on top of your window sill, with supporting brackets, as well, to make room for a slightly deeper width tank.
Another thought is if, for some reason, the tank doesn’t work out in front of a window, you could mount it on a wall with heavy duty floating shelf brackets and have it be a living piece of artwork - even put a picture frame around it! I believe there are some commercial tanks available like this.
I would absolutely try this idea - maybe even make it a Scapecruch challenge!