I have a campaign coming up and I want to use an artificer from one of the sourcebooks, I was wondering if I could buy only the subclass on the app, is it possible?

You can buy the subclass through the Web browser and it will appear in your app. I don't see a way to do it in the app directly, though.

Looking at the app on my phone specifically, I'm not seeing the piecemeal content available.  I do know that if you're on a computer and using the web based marketplace you just click on a source, scroll to the bottom of it's page and you'll see piecemeal content available to buy an individual subclass or even an individual spell.  You might know that and were asking specifically about the mobile app.  If that's the case, sorry and I don't personally see a way into piecemeal content from the app's marketplace.

The app is very limited in what it can do, It isn’t designed to work with DnDBeyond.com in real-time, etc. The app is really only designed for people to be able to access their PCs & compendiums without internet connectivity and then sync nightly with your device’s native nightly sync.

So if I were to buy it from the app would it appear in the web browser I want to buy the bf one but have been having trouble with the browser and my card so I want to get it via the app but I wanna make sure it'll appear in his web browser

He will be able to access it on the web, but it won’t appear under the list of purchases on the web. It’s goofy. However, I strongly recommend against purchasing anything through the app as it can often take quite some time for purchases to be processed by the App Store, like on the order of days.

Interestingly, some content is substantially cheaper on the app than the store - despite there being extra costs involved. Not sure why, but I'm tempted by that to buy one of the books.