What was cutting edge 100 years ago would be beyond out of date...
Not necessarily. The rate of innovation is not a universal constant. If anything, historically, the norm has been a fairly slow rate of progress, only minor and gradual improvements in techniques, with bursts of rapid innovation being atypical. And if you really compare TOS tech to TNG, there aren't really many material advances in physics or technology. The warp drive is faster, but it's still warp drive, using the same principles. The transporters have longer range and biofilters, but they're still transporters. The phasers have more powerful settings, but they're still phasers. They have replicators, but those are simply a refinement of transporter tech, based on the same principles. They have structural integrity fields, but those are a refinement of forcefield and artificial-gravity tech. Sensory prosthetics are more advanced, but Geordi's VISOR is basically a more powerful equivalent of Miranda Jones's sensor web. Computers use optical chips, but they don't seem that much more sophisticated or powerful; if anything, they seem to be
less intelligent at times, since we don't have things like "Day of the Dove" where the crew asks the computer to explain the plot to them and suggest a strategy.
Meaningfully new technologies in the 24th century are few. Holodecks are the most prominent one, although if you accept TAS: "The Practical Joker" and disregard early TNG's references to the novelty of holotechnology, you might see a 23rd-century precedent there (and ENT has established that Earth had some limited holotechnology over a century before TOS, since there was an episode where they used a holographic target drone -- and that's not counting the Xyrillians' holotechnology in "Unexpected"). There have been breakthroughs in artificial intelligence -- Data, Moriarty, the EMH -- but one of those was near-unique and the others were accidental; and besides, Scotty certainly encountered sophisticated alien androids from time to time, so he has some prior knowledge in that field. I suppose the single most significant sea change in technology between 2294 and 2375 would be the bio-neural gel pack.
So evidently the Federation has reached something of a technological plateau, experiencing far less innovation in a century than we have in our current period of atypically rapid progress. Most advances made during Scotty's, err, extended vacation were matters of degree, improvements upon familiar principles rather than fundamentally new principles. So it wouldn't have been anywhere near as hard for him to adjust to the 24th century as it would be for an engineer from the 1930s to adjust to the present day.