Unless you've been saving your projects somewhere into "Logic Pro X" app package located in /Applications folder (which I doubt), removing the app itself from your system won't remove the project files. Removing / uninstalling software in macOS works a bit differently than in Windows. Basically, what you've been asked is to move "Logic Pro X" app from "Applications" folder to Trash (and then emptying the Trash, of course). That's it, everything else, including your saved project files, should be left intact.
Also, switching from trial to full version doesn't negatively affect projects created while using the trial version, quite the opposite, I should say. As you'll be able to use all built-in software instruments, FX and sound library content without limitations in your projects after you switch.
However, just to be on the safe side, make sure to back up your project files to an external HD / USB drive. Regular backups of your important data to external drives is a good practice, anyway.
Also, a useful tip: before removing the trial version of Logic Pro X app from Applications, right-click on it and choose "Compress Logic pro X" from the drop-down context menu. This will create a ZIP archive of the app package, which you could copy somewhere else on your system HD or to an external drive. If anything goes wrong with Logic Pro X app after switching to full version, you will be able to go back to the previous version of the app just by extracting that archive into Applications folder. This also applies to a situation when you'd want to make a backup copy of the full version of the app (e.g. before updating or upgrading it).
