Neat top break
Actually... Smith & Wesson introduced the .38 S&W cartridge in 1876 as a round to be used in top-break pocket pistols, the original loading was a 145 or 146 grain bullet and black powder.
I have a very early production S&W Safety Hammerless(Lemon Squeezer) and a Model 2 double action that take the .38 S&W round.
The Brits designed and used it originally with a lead 200 grain bullet, basically a British copy of the .38 S&W Super Police round, which popped on the scene in the '20's. The Super Police round was slightly hotter and a heavier bullet than the original .38 S&W, and not recommended for use in the older pistols. Now with concerns about Hague Accord violations, a revised FMJ bullet weighing about 30grains less was designed and used. So while the .38/200 name stuck and was also to differentiate it from the .38 Spl rounds that were common at the time and used in the Victory/Model 10 revolvers. After the revision, it became a 170ish grain bullet, it was also known as the British .380 Mk II.
And yes, the .38 S&W is....down loaded. There are thousands of old S&W, Iver Johnsons, H&R and other top breaks that are 110-130+ years old in circulation, that were designed in the black powder days. Not a good spot for super hot smokeless rounds, I have fired Fiocchi in mine with no issues, it is kind of anemic if compared to modern ammo, even a Russian Nagant.
For your beefier design, I do believe .38 S&W Super Police can be found in some boutique ammo retailers, that would possibly be about as close to the original loading you will find, short of some high dollar .38/200 or .380 MkII British surplus.