You are quite correct there is a linear drain that runs along the back wall, the small mosaic tiles fitted inside it, albeit quite tricky.

Is the glass shower wall custom, or is it metal framed windows used as the shower wall?

It is most likely a custom shower glass and wall frame. Probably most financially sound, since large glass for showers are a bit thicker than window panes (even when they’re required to be double pane for efficiency and storm-security).
But I wonder if it’s a single piece of glass with frames around it. That would make cleaning a bit easier, but also drive up the price for custom water-proofing framing. Without the framing, cleaning would be a breeze! Well, at least more so than with.