WordPress can embed both YouTube and Vimeo videos that are public and “unlisted”.
A search for “video” in the Blocks area yields a lot of options.
Admittedly, it’s confusing to have so many options to embed a video on your WordPress page. I would ignore the “Common Blocks”. Here is some guidance for the other options:
Embeds
Vimeo: Use if your video is hosted on Vimeo
YouTube: Use if your video is hosted on YouTube
Note: Your videos need to be public to show up.
Reusable
Video__Two Column Video Text:
You can see what that looks like here.
Video__Full Width: This is actually duplicative of the YouTube Block
Banner__Video Background with text Overlay: This allows you to put a title over your video with a transparent overlay to ensure text readability. See a sample of this at the bottom of this page.
From my experience, all of the embeds scaled responsively to different breakpoints for desktop, tablet and mobile. Just something else to watch out for.
This is how a video imports from Class WordPress into Gutenberg WordPress.
Learn more about social embeds, YouTube and Vimeo embeds and video styles and WordPress Embeds in general.