I'm afraid I can't recommend a single over-arching narrative history of steam transportation.

For steam engines, Henry Winram Dickinson's 1939 A Short History of the Steam Engine is a classic, despite the title probably has everything in it you'd care to know, and is still available.

There are some pretty decent histories of steamboats, like Louis C Hunter's Steamboats on the Western Rivers, but not for the earliest designs of them: James Flexner's Steamboats Come True is readable and not too terrible and copies abound, but it suffers greatly from embroidery ( he was an art historian, and perhaps therefore had to fill out every scene with imagined details) . Andrea Sutcliffe's Steam was not in print that long, but was a credible effort. But there's a big problem with sources, for this. There's only one very copious source ,John Fitch's memoirs, but they are quite biased. There's almost nothing by his rival James Rumsey, and a vast empty spot in the records from the 1836 US Patent Office fire. As a result, authors wanting to get their work done have tended to use Fitch's account uncritically, starting with his first worshipful biographer, Thompson Westcott. If you can find it, I'd use Sutcliffe. She also makes uncritical use of him, but at least doesn't make it all his show.

There are hordes of railroad fans out there and so zillions of oh-my-ain't-this-gorgeous books. I have not been able to keep up, but John H White's old American Locomotives is something of a classic, has tons of great period drawings and a little history, and is reprinted by Dover and so good value for money. Recently, Ken Gibb's Steam Locomotives: An Engineering History is a good attempt, plenty of mechanical details: but it's an engineering history, as it says, and doesn't venture into the social history of the railroads...which is huge, and I can't guide you on that. .

Just looked, and it seems Sutcliffe's book in now offered for Kindle.