On the right, you'll see a column named "64-bit (Intel)." If you see an app that says "No," you may run into some issues. You can click the column tab to sort the apps so you can see all the no's in one group.
For apps that show "No," check the column named "Obtained from." If the app says it's from "unknown," it may not work in macOS Catalina. Those that are "obtained from" Apple, the Mac App Store, or an "Identified Developer" are much more likely to be available in 64-bit for macOS Catalina, even if the app is 32-bit on macOS Mojave.
If you want to make sure an app will be compatible with macOS Catalina, Apple's advice is to contact the app's developer.
In Apple's own words:
"The easiest way to contact a developer is to look them up on the web. To find the name of the developer of an app, select its icon in the Finder, then choose File > Get Info from the menu bar."
Or, you can try Googling the app's name with "64-bit support" in the search term and see what comes up. The move to macOS Catalina shouldn't pose massive problems for most people, but it could be messy for those who use more obscure apps that might not be updated so frequently.