Hello TechNoobRomance,
Thanks for asking the Apple Support Communities for help with Text Edit and Preview not closing properly. I am happy to help.
1. I recommend booting the computer to safe mode. Safe mode will tell us if the issue is related to a startup item or plugins, and sometimes is all that is necessary to correct some problems.
When you boot to safe mode, log in to your account and check if the issue is also occurring in safe mode or not. Use this article for the steps to get into safe mode: Use safe mode to isolate issues with your Mac - Apple Support
If everything is working properly in safe mode, but then is not working after you restart the Mac, please check the section titled "If an issue doesn't happen in safe mode" for the next troubleshooting steps.
2. If the issue is also occurring in safe mode, move on and test if this problem occurs in a newly created unmodified test administrator user account on your Mac. A test user will let us know if the issue is isolated to your account, or system wide. Please check this help article: How to test an issue in another user account on your Mac - Apple Support
After you are done testing, please check the section related to results, titled "If the issue happens in the other account" or "If the issue doesn't happen in the other account”.
Thanks again and have a great rest of your day.