There are a few seconds of Fallout TV show clips on the FireTV/Prime Video Home screens that aren't in the trailer.

On FireTV, an outdoor market in a green area, and Vault Dweller wielding what looks like an Auto-Axe.

Anyone got a good video capture device?

also, other different moments are shown in the menu background at [Automod won't let me link to Amazon, the site the show is on...]

If you browse Prime Video to where the show will be, you can see it, but it looks like you have to be signed in to Amazon.