Poked at this a bit and the best source I could find was an old article from the LA Times: https://www.latimes.com/archives/la-xpm-1990-08-30-fo-320-story.html. This isn't an academic article but after looking up the author I found that he is very dedicated food researcher and historian who has translated medieval cookbooks from Arabic into English, has written scholarly articles, and is the founder and president of the Culinary Historians of Southern California, so I'm going to trust what this article says, specifically this bit:

"Mostly malt is fermented and turned into beer or whiskey. However, malt sugars are easy to digest, and 19th Century doctors often prescribed malt for children and invalids. There were problems with it, though. In liquid form it tended to ferment, and for years every attempt to produce a stable dried form of malt failed."

Let me provide some additional context for this. A lot of drug stores would sell malted drinks to sick people or children out of the belief that malted drinks are easier to digest than the grains that they're made of and this would help nourish those people. This does have some truth to it. Maltose, the main component of malted drinks, is a much simpler carbohydrate than the starches of grain so the body can digest it quicker. However, glucose is an even simpler carbohydrate than maltose and is very easy for the body to digest but I doubt that it's a good idea to give sick people a bowl of glucose syrup for their nutrition.

But, in any case, maltose is a simpler carbohydrate than grain starches. This not only lets humans digest them more quickly but the same applies to yeast as well, which have a hard time eating starches but love maltose. This is why people malt and mash grain: to provide food for yeast to make beer. Very give a simplified version of how this works you do the following:

1. Take some grain.
2. Let it sprout a bit.
3. Remove the sprouts. Then it's a good idea to lightly roast the grain so it doesn't rot.
4. Cook the grain in water a very specific temperature (63-70C) for an hour or so.

This cooking (mashing) allows enzymes in the malted grain to break down the starches in the grain. Depending on how many of these enzymes are present (or the diastatic power of the grain) the enzymes can also break down the starches of unmalted grain, potatoes, or whatever else you threw into the mash. Breaking down these starches produces maltose which yeast can eat so if you add yeast to this unfermented beer (called wort) it will ferment and turn into beer. I'm skipping a few details but that's the general idea.

Now what happens if you drink this wort (unfermented beer)? Well it tastes very sweet since maltose is very sweet until the yeast eat it up. So now you've got a tasty sweet drink that you can sell.

There's just one problem. This sweet drink is not only tempting to people with a sweet tooth but also to yeast (who would just love to turn it into beer) and bacteria. Having a drink that can easily spoil is a big problem which is why that even though this drink DID exist in the 1830's and seems to have been sold in pharmacies as a healthy drink for kids and sick people it wasn't as popular as it became later. Kid probably would've loved it because it was certainly quite sweet. And while mashing temp is a lot lower than boiling the process of mashing the malt is hot enough to kill off bacteria so if you get some fresh malt drink it should have less of a risk of infection than unpasteurized cow milk.

But what to do about the bacteria? Well there are three options:

1. Keep it cold. Bacteria and yeast can't grow well in the cold. But people in the 1830's didn't exactly have reliable refrigeration so this is right out.
2. Pasteurization: basically cook the malt drink (or milk or juice or whatever) at a high temperature and then immediately stick it in an airtight container. This isn't perfect which is why pasteurized milk eventually goes bad but it's pretty good and people in the 1830's certainly had the technology to do this. And there were example of people using heat to kill off bacteria before, it just wasn't something that most people thought to do this early.
3. Take out the water. Yeast and bacteria both need water to live. This is why you can keep a bag of sugar that isn't even airtight and it won't get stuff growing on it but wet sugar will get bacteria and other things growing on it quite quickly.

It seems that people tried to do #3 early on with malt but ran into trouble. The article I linked says that early attempts weren't shelf stable (which means they would go bad). The other issue is that barley malt is (as any homebrewer who's worked with malt extract will tell you) just incredibly sticky. If you take some unfermented beer and boil it down the heat of cooking it will caramelize it at least a bit before all of the water is gone. Even uncaramelized malt syrup is very sticky and difficult to deal with but with caramelized malt syrup you'd end up with a bottle full of a glue or even have it stick solid. Not easy to work with in either case.

Then William Horlick came up with a smart idea to fill a container partway full with liquid and then pump the air out to create a vacuum. This vacuum would suck the water out of the liquid (as water vapor) without having to cook it. He could keep on doing this an the malt would eventually turn into a powder. A nice shelf stable and easy to work with (and only somewhat sticky) powder. You could do the same thing with milk to and make powdered milk that would keep for a very long time. He started mixing malt powder, powdered milk and a bit of flour together and selling it for kids and sick people.

It caught on. Eventually people started mixing ice cream in as well and this became hugely popular and you can see it in older movies in which teenagers order "malts" or "malted milkshakes."

But what did those 1830's malted drinks taste like? Something in the right ballpark would be Korean sikhye which is made with malted barley and rice (so half right). It's a bland sweet milky drink with bits of rice floating in it. You should be able to find it at a Korean food mart. The other option is to get some malt syrup, mix it with some water and drink that. You can find barley malt syrup online and at homebrew stores. It's sometimes used to sweeten baked goods or used as a sugar substitute for dubious health reasons. Rice malt syrup is also used a lot in Asian cooking while high-maltose corn syrup is the corn equivalent (but it has a lot less flavor than barley malt syrup). There's also wheat malt syrup but I don't think I've ever heard of it being sold anywhere besides homebrew supply stores.