Dear all
My laptop was not sleeping upon lid-close. The problem turns out not to be specific to some one Framework model or even to Framework laptops. The problem seems rather to be something in Linux Mint (or at least Linux Mint Cinnamon edition). Please see here on the Cinnamon bug tracker for a script that aids troubleshooting of the problem and for a (fairly painless) workaround. Still: your milleage my vary with the workaround. It seems to be working for me.
PS: Moderators: this post is unhelpfully tagged, but I cannot manage to tag it more helpfully. I will be creating another post - well, I will if I can tag it such that the system lets it through! - about the nightmare of tagging.