Adding images to forum posts

I know we can embed an image into a forum post via upload, but is it possible to choose an image (or multiple images) from the gallery?

This method won't be as easy as being able to directly select from a list of images, but you could add the main_gallery_embed block to your forum post. If you click the Add Block icon in the forum post editor and scroll down to the Galleries section, you will find the main_gallery_embed block. The block settings include Image Filtercode and Image Selectcode which you can use to filter which images will display.