Two things done to the clips you sent, for the site's background moments: steadied the camera shake (so they feel calm and shot-on-a-tripod), and made them loop so they play continuously with no obvious restart.
Left is your original clip. Right is the finished version — steadied and looping — as it would sit behind the titles on the site.
A note on looping: a clip can only loop invisibly if it has a calm, repeating feel (greenery moving, water, a quiet view). If someone walks through the shot there's no moment that repeats, so it can't loop seamlessly — those are best used as a single play, or we pick a calmer clip. You'll see that on the one below with people in it.
This is the process going forward — send the clips and I'll steady and loop them the same way for the site.