Click YouTube from the insert menu. You can search by entering a word or select from your uploaded videos.
To insert a single video like the one above use the From Drive option and select the individual video. Make sure to share the file publicly or 'anyone with the link can view'.
Used the embed code function to see if it works better in iPhone. Note that fullscreen doesn't work unless you click the pop-out icon and view it that way.
<iframe src="https://drive.google.com/file/d/1bRNbZe1Te2u8zhDd_A6V-ja51Ll9ZJ-g/preview" width="640" height="480"></iframe>
Use the YouTube section in the Google Embeds section of the Insert menu. Select 'Uploaded' to find your own or use the URL you get from the share function under a video.
To remove the related videos showing at the end if the video see the video at the bottom of this page.
Video hosted on Vimeo. Note that full-screen works (it didn't work on classic sites).
Get the Share URL for the video and use the Embed URL function in the insert menu.
To insert YT video, not my own, I got the URL by clicking the share button below the video and inserted it by using the embed URL edit function. URL: https://youtu.be/_H6nNysTQs8
To remove the related videos showing at the end if the video, view the video in YouTube, click share, select embed and in the options remove the check from "Show suggested videos when the video finishes". Click Copy to copy the embed code. In your site use the code section of the Embed function and insert the code.
Note that this option may have been removed. Also full-screen is not available when using this method.