From my checks, it seems like Google is seeing this (and other content) properly on your homepage.
It looks like the entire website content is loaded in via JavaScript. In other words, if you disable JS in your browser and refresh the page, nothing appears. This is way when you view source you won't see that text. You're absolutely right in checking inspect element!
There are a few ways to check whether GoogleBot is seeing the content you want it to see. GoogleBot will take a "snapshot" (something called the DOM) within 5 seconds of landing on your site. What we want to do is get as close to the DOM as possible.
Here are some ways to check if GoogleBot is seeing your content properly.
1. As Gaston mentioned, you can use Fetch and Render in GSC. I've heard that a better option is to use Google's new Rich Results Tool input URL -> run test -> view source code -> copy HTML and search to see if the content you want Google to see is there. From my understanding the reason is because the new tool spits out the DOM (that snapshot) while GSC will not.
2. You can load the page -> inspect element -> right click on the opening at the top -> copy -> copy outerHTML -> paste into text editor. Then just search for the content you want Google to be seeing.
3. You can use a tool like Screaming Frog and select JavaScript crawling to see what a different crawler can pick up.
4. In this case, since we're just looking for text, we can also just search for the exact text in quotes in Google search.
TL;DR - from my checks, Google is seeing that specific content the way it should. However, since the entire site is loaded in via Javascript it will be vital to continue checking on other elements (like internal links, etc). Hope that helps!