Google Photos now has a new auto-enhance feature you can access, which analyzes your clip and then applies its own choice of color enhancements, while stabilizing the video at the same time.

Tap Video then Enhance to apply the automatic enhancements.
Tap the play button to see how the updated footage looks.
Tap Enhance again to see the difference with and without the tweaks.
Choose Save copy to save the enhanced video as a separate file.