make half sheet document

I create a lot of "card size" images (I make my own birthday, holiday, etc. cards). I simply use a regular size sheet in Pages or Swift Publisher, create my card, and then use Command + Shift + 3 to outline the finished part of the card and save that. That'll open in Preview and you can save/convert that if you wish to pdf or jpeg or whatever else is offered.

Why not make a custom post card in Pages v7.3 File menu : Page Setup…, and then set your landscape Pages document to that custom card size. Once you have finished the card content, then simply export as PDF, and attach to the email. The PDF will open as a post card sized entity. There is a dedicated Pages for Mac Support Community available to you.

See what happens when you drag a jpeg into mail and send it. Could you have been using a different email client than mail?

You can set the background in mail:

I use thunderbird too.

To make a 1 page PDF file as an attachment and not displayed in the email's body either put it in a folder and add the folder to the email or zip/compress it and add the zipped file to the email.

Multiple page PDF files will display as an attachment icon.

To get the postcard page, i.e. 8.5 x 5.5, create a custom print size.

In Pages make the first page your postcard and then add a second, blank page.

Save as a PDF and add it to the email. It will not be displayed inline but as an attachment.

Sorry - I said 3, it should have been command + Shift + 4 which will automatically create a square or rectangle (however/whichever area you drag your cursor around) like I did here of part of your post:

And, I created a "card" - it is a regular size doc created in Pages (with the image about 1/3rd the size of the 8 1/2 x 11, exported as a pdf in full size (and it would not allow me to post it, probably too large). I then opened it in Preview and used command + shift + 4 to get this - just the image itself: