Not sure about the entire world. But the real change from steam to internal combustion in the US began to happen around the late 1890's. There had been a continuous effort to make reciprocating steam engines more thermally efficient, and the solutions were making them more complex- and they still could not get them past about 18%. While an internal combustion engine could get twice that efficiency ( in theory if not often in practice) the complexity was a bigger problem, as was the size of the engine and what it required. For example, to fit up a steam engine on a New England fishing boat there had to be space for not only the engine but the boiler, allowance made in the deck for a smokestack, ventilation below ( as it could get very hot in the boiler room), a maze of pipes, possible outside condenser, numerous gauges and a trained guy to make it all work. But a small hit-and-miss gas engine and small gas tank could easily be installed on a tilted pad near the stern transom, and the few horsepower it supplied was invaluable for getting the boat in and out of port, even getting it home in a dead calm: and it could quickly be fired up by someone with minimal training who didn't have to be constantly minding it as it ran. Huge numbers of small machine shops turned out small hit-and-miss engines, and huge numbers of small-to-middle size boats were fitted up with them. Large ships with the space would still continue to use steam- especially once steam turbines ( and the gearing needed for them) were developed with far greater efficiency. Many if not most of all of those would switch over from coal to hydrocarbon fuel oil, saving the need for dozens of fireboxes, armies of stokers and bunkers of coal. That largely began to happen after WWI. The famous Liberty ships that were mass-produced for WWII had reciprocating steam engines, but the not-quite-as-famous-but-faster Victory ships produced later in the war had far more efficient steam turbines.

Likewise, the hit-or-miss engine could be added to a farm, where it could be in residence to saw firewood or run a threshing machine. It was far cheaper than the big steam traction engines, that usually were hired for a harvest and also had to have a trained operator.

Factories with steam engines running line shaft machinery also went from steam to diesel. Or ( very commonly as the electric grid was extended) simply switched over to electric, which needed even less maintenance than an internal combustion engine. The last to change over were the railroads. These not only had a huge amount of rolling stock that was steam-powered, but a whole support system of shops, warehouses of parts, and trained technicians. Some, like the Norfolk and Western, would also build their own locomotives. And of course trains could run on coal- and some railroads even owned their own coal mines. All of this existing equipment and infrastructure created a lot of inertia, meant that changing over to diesel had to be gradual in order to be cost effective. The Norfolk & Western was ( I think) the last to do so, running their steam trains even in the 1950's- which happily gave photographer O. Winston Link subjects for his now classic steam photographs. The switch from coal to diesel saddened fans of steam engines ( no disputing that there is something really cool about a steam engine- making miniature ones have long been popular for home-shop machinists), but there were few regrets from the crews who had to actually work on them. The shops noticed the difference: it would take them a few minutes to figure out what was wrong with a steam locomotive but days to fix it, whereas it might take a few hours to figure out what was wrong with a diesel and a few more hours to fix it.