I’m a bit confused here. Usually watermarks are used to reduce the commercial value of an image or video. It doesn’t affect copyright. It is unlikely that someone can claim adding a “do not copy” watermark to an image creates a derived work. And a “do not copy” watermark is likely not creative enough to have its own copyright.
You may have permission to reproduce the video with watermark, but that depends. If not and if the video is copyrighted then it was copyright infringement. Damages may be lower because of the lower commercial value.
PS. Since the video is your own: It happens that a free (no cost) video adds a watermark, so you can try it out, but cannot use it commercially. Like you wouldn’t want a watermark in your wedding video; if you pay for the editor the watermarks go away.
As I said, it is unlikely that the creator of the watermark can claim copyright, because copyright requires a creative process and the watermark will have very little creativity. It is even less likely that the creator of the watermark takes you to court about it and wins, or sends a DMCA takedown notice. They are not interested in that. And others can’t accuse you of copyright infringement.
If it is like an advert for the software, they most likely want you to make as many copies as possible. That would be in their best interest. You may have a license that actually allows you to duplicate the watermark.