Can I copy a video strip from one opened Blender into another? I have a project where I have a video, I added to that video some text and I sped it up. I want to re-use that project/video within several other projects.

At the moment I have 2 blenders opened. One with that project, and another one, an empty one where I want to copy it. I tried using the append feature, and appending the scene, but that only appends a cube, not the video.

I could render into a movie, and then reuse the movie, but wouldnt that lower the quality?
This works for me - pack the video into .blend using File -> External data -> Pack All into Blend.
Then from the other project select File -> Append, find the .blend with the packed videos and append the Scene datablock.
The video strips should be appended now.