In my last house I had an instal similar to the first picture but obviously didn’t have anything overhanging the stove or likely to melt! Wtf are they thinking?
The top section of twinwall was not noticeable, the rest was single wall and it gives off a lot of heat. Downside is a fire board wall section and care to insure no combustibles eg studwork are within the zone around the flue.
Draw was phenomenal, unlit the stove door would pull itself shut at the last open inch or so.
I would strongly recommend getting up to speed on stove install regs to get your head around what is permitted and safe. Loads of stove manufacturers show pictures of their stoves installed in a way which may not be permitted in the UK.