SE sites (that aren't in beta) have "community ads", which are ads submitted by users on that site for things they think will be of interest to other users on that site. Some use them to promote SE-specific things like sandboxes or weekly chats. Some use them to promote external resources of various sorts (conferences, reference materials, professional associations, etc). A few use them to promote Codidact communities. This is all perfectly within their rules.
In order to be used, an ad needs a certain number of votes from users on that site's meta. We can submit ads on relevant SE sites (and obviously some of our members have done so). We don't want to be spammy, so let's not promote, say, our Cooking community on English Language & Usage, but promoting related communities like in your screenshot is fine.
These ads will do better (i.e. are more likely to reach the vote threshold) if they're submitted by people who are users on those SE communities. This doesn't require the Codidact team specifically to do anything; further, if we were to post everywhere, the chances are higher that SE would accuse us of spamming and block us. Advertising like this is best done organically and can be done by anybody. You can use the ad templates linked in the right column on the community you want to advertise, or you can roll your own. Some of our earliest ads on SE were made with custom images, before we had the templates. Do whatever you think makes us look good, following the rules on SE for community ads.
Stack Overflow has different rules than other communities. They accept ads only that promote open-source projects. We have an ad there. The ad links to our Github repository; it's advertising for contributors, not community members.