Can I put a video in my email so it plays inside the message?

No. A playable video cannot be placed in an email, except as an attachment, which people do not want.

Instead, use an animated GIF made from your video, which makes it look like there is a video in the email. You can ask the AI assistant to make the GIF, use the GIF maker in AI Image Gen, or use an outside tool, then add the GIF to your email.