I'll wear the dunce cap: how are you so certain this is co-marketing? I'm not saying you are wrong, but it doesn't seem obviously like marketing copy to me (which is of course what they'd want but that's nevertheless not in any way evidence one way or the other).
It starts with the words "As part of our continued collaboration with Anthropic"
Once these words are used you can assume there is a contract stating how that collaboration works, and that this includes some sentences about how much each side is allowed to or required to say about it
So you claim that Mozilla entered into a contract with Anthropic, and said contract requires Mozilla to advertise for Anthropic on their blog. I hope Mozilla is getting a good payday out of this.