Add: first hit on youtube is nice https://www.youtube.com/watch?v=z3okBYfi2lg
Clearly not enough of an advantage to keep using them, but Waverley was built for a route already being serviced by a fleet of three other paddle steamers, and presumably a screw ship would've required some operational changes, so it's easy to imagine the company deciding to stick with what they knew rather than get with the times.
It does make me wonder if there are other advantages, like what kind of engine disturbs the environment the least.
Then there's other things like channels having been dredged over the years, roads have been massively improved, ships have echo sounders etc., so maybe there's less need nowadays for traversing really shallow waters with big boats.
I heard about Waverley when I visited the Maid of the Loch https://www.maidoftheloch.org/ which is a paddle steamer that they are currently repairing at Loch Lomond where it used to do trips.
Had an impression on me when I first went on it and still does whenever I see it.
"In the 1890s, British shipyards built seventy-five percent of ships worldwide, two-thirds of which came from Clydeside"
https://blogs.loc.gov/inside_adams/2017/09/clydeside-shipbui...
FWIW, a similar percentage of the world's steam locomotives were also made in the area in the same timeframe. Mind-boggling concentration of the worldwide heavy industry at the time!
Looks like that would have been the new Riverside Museum (very distinctive Zaha Hadid building in an open area) rather than the old Transport Museum?
For anyone reading this thread, I highly recommend visiting the Riverside if you get a chance, as well as the Tall Ship moored next to it, which has been developed into an excellent historical museum in its own right in the last few years.
Ah yes, that must be it, looking it up online I recognize the building. It appeared very shiny and new when I visited, which seems to match the timeline (per wikipedia, it opened in June 2011, and I was there in spring 2012).