It's very hard to stabilize a 360 video, whether in spherical or equirectangular format.
The 2D zoom effect will not work, obviously, but if you really need to remove some serious shaking, here's what I'd do (equirect):
- Apply the stabilize filter on the video
- export the resulting video
- re-import the stabilized version
- apply it as a new layer in the center of the video, with reduced size (e.g .90% scale) so that you can see the original around.
- hope for the best.
1. you'll still have a shaky video on the top/bottom + back of the video.
2. You'll see distortions, as the spherical map shifts a bit, especially in the upper-lower regions.