When I email photos, the captions aren't included. I have Adobe Photoshop Elements 2019.
In the organizer: File >> save metadata to files (shortcut Ctrl W). You write metadata to files, not only captions but also tags and ratings.
Whether you want to email your photos or not, the problem is to create a new image from a photo with an added text. If you have created that image, you can email it if you want.
Adding text to a single image is an easy and interesting task in Elements and you can have hundreds of ways to customize the text, its position in or outside the image, the font choice and size, the best location for the text depending on the image content. What is another problem is to find the way to automatically add the same text to a batch of different images. It's another problem if the text on each image is coming from metadata with different text length.
The only automatic process for that in Elements is an option in the printing dialog to add the caption. The formatting options are extremely limited, good enough for creating 'contact sheets'.
That option is only for printing at home.
The final word is that while you can customize creating a new image including the caption freely yourself, there is no automatic way to do so automatically for a batch of files. You can't email a file which has not been edited to include the caption in the image either.
My previous version of Photoshop Elements - maybe version 8 would automatically include each caption with each photo. If I understand you correctly, the current version "2019" cannot do this?