If you DELETE the photos from your album, it deletes them from the cloud too. If you use the "Free up space" option in the Google Photos app, it will remove the videos from the memory on the phone but keep them in the cloud.
Here's an example video zoomed to about 1.8x. The shaking is from the camera mount and my big ass taking out the slack, not from the imaging hardware. https://photos.app.goo.gl/MxWHSbiTvmDDuq1u7
The other cool thing about hosting your videos in Google Photos is it uses the Youtube player to view, meaning you can slow down to 1/4 speed by clicking the little gear icon in the lower right. But when you do that, you wish you had a higher frame rate camera lol
This is a Google Pixel first gen. Starting in the second generation of the Pixel, they introduced image stabilization that would cause all the funky video effects. I haven't tried my current phone, a Pixel 5, with what BobF suggests, but I think I'm going to.