Should I make a new video for every application?

You definitely do not have to make new videos for every job you apply for. In fact, it is better if you only make one video that is applicable to all the jobs you are interested in.

When you submit an application for a job, the manager receives a link to your profile. Any updates you make to your profile afterward will also be updated in your application. This means that the manager of each job you apply for will see the same video. Your video should be generic enough that it will be relevant to all the jobs that you apply for.

Good luck with your job search!