It's still very much a work in progress, but I have just created @[email protected] with the intent to automatically post the daily game posts, rather than people need to do it themselves.
For now it's just Connections as I'm still working out the kinks (it didn't succeed in getting it up the first time today...I had to stop and re-run it to get it to work). But I would like to expand it to some more games later: post suggestions in the comments.
Lemmy has a setting to hide all content created by bots. If you wish to join in the Connections (and possible other future daily games), please make sure you have "Show Bot Accounts" selected.
I think it's a good idea for a/the bot to post the more popular games daily in a single post, it also allows for more obscure (posted less often) games to be highlighted by having their own threads!