Hey there MattGlow,
Thanks for asking the Apple Support Communities about issues with Quicktime on your Mac.
First, try a restart of your Mac, as that can solve many problems: Shut down or restart your Mac - Apple Support
Next, update. For macOS 13, the latest update is 13.4.1: Update macOS on Mac - Apple Support
Check here next: If an app freezes or quits unexpectedly on Mac - Apple Support
Next, you would test this in safe mode. Use this help article: Try safe mode to isolate issues with your Mac - Apple Support
If you no longer experience the issue in safe mode, but it occurs again after you restart the computer to leave safe mode, please check the section titled "If an issue doesn't happen in safe mode" for troubleshooting steps.
If the issue is also happening in safe mode, you want to test this in another 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
If the issue is not being experienced in the test user, check the section titled "If an issue happens in only one user account" from the article provided in the previous sentence of this paragraph. It has a few things to check, but then leads to this help article: Mac OS X: How to troubleshoot a software issue - Apple Support
You also want to try recording a Quicktime video without the third-party products connected to the Mac. If Quicktime works without the third-party products, you will need to ask the manufacturer for help with their software or hardware. It's possible it's a cable issue, or port issue too. Try connecting those items with another cable, and to another port to test also.
When was the last time you were able to record a video while using the app you mentioned at the same time, and does this only occur when opening the teleprompter app while recording a video in QuickTime on your Mac?
Thank you.