Sweet, thanks!
Using this markup I think I was able to achieve what you were asking for:
.site-main .wp-block-group__inner-container {
display: flex;
flex-flow: column nowrap;
height: 100%;
}
.site-main .wp-block-group__inner-container .wp-block-buttons {
margin-top: auto;
}

But this is not ideal, it's merely a quick and dirty proof of concept. I have a couple of follow up question, since It's a been a while I worked with WordPress:
-
Is there a way to make the columns "stretch" because they currently don't fill their container:

If there is, please remove the
height: 100%css markup. -
Could you add a custom class to the columns? Otherwise the markup will apply to all columns on your site.
-
Could you add a custom class to the button? Otherwise the markup will apply to all buttons on your site.