QuickTime Player gets stuck when I use it with Apple Magic Mouse

I'm sorry, I cannot replicate your issue. my Magic Mouse is working as expected with QTP. so I need to ask, do you have any antivirus apps installed? or any app that claims to "clean up" or "speed up" or otherwise "optimize" your Mac? apps like those are neither needed nor recommended on a Mac. they are known for causing issues within macOS, while providing ZERO protection or benefit. if you do have such apps, you would do well to uninstall them using the developer's instructions.

but if you have no such apps, i'm thinking you should download and run the free version of EtreCheck so we can see if you have some software installed that is causing your issue. make sure you give "full disk access" to etrecheck. Learn how to use it by reading Using EtreCheck. if you need help interpreting the report, you can see how to post the report here by reading How to use the Add Text Feature When Posting Large Amounts of Text, i.e. an Etrecheck Report. and it automatically obscures sensitive things (like serial numbers) so you don't have to worry about sharing the report here.

sorry, I missed the "Touch Bar" reference in your original post. I'm on an iMac, so no Touch Bar here. I will not be able to test your specific steps.

but you also said this:

These steps worked on my other friend's MacBook as well,

does that mean it is working properly on your friend's MacBook? or does that mean they are seeing the same issue as yours?

if it works properly on the other Mac, then it indicates that you may have some software on your machine that is interfering with QTP functions. so I will again ask if you could share your etrecheck report with us.

but if the other Mac is having the same issue as yours, you might need to file a bug report with apple. please see Feedback - macOS - Apple