@ilfelice: thanks, that's the kind of objection worth having early. Let me propose a rule that I think answers it, rather than argue the original post. 🙂
Official material carries the logotype and the claim only. No mascots on the logo, the site, GitHub, the documentation, or the ISO. One mark, consistent across every touch point, which is what you described, and I'm not going to argue with thirty years of it.
The mascots live in informal material, such as social posts, wallpapers, stickers, event graphics, and blog illustrations. That's where a project gets to have a personality without putting anything at risk, and it's the part that never touches the brand's primary surfaces.
If that line holds, I don't think the dilution case applies: nothing competes with the logotype, because nothing else is allowed anywhere the logotype does its work.
One thing worth keeping in view, from @Bob 's point: the dog is the Tracker icon, from BeOS through Haiku. That's not a mascot we invented. It's the one mark this audience has recognised for twenty years, and "Continue" is exactly that continuity. Inherited equity is worth building on rather than redrawing.
@ilfelice: if you're willing, the part I'd genuinely value your experience on is where that line sits in the awkward cases. Is a default wallpaper official or informal? Release notes? Those are the places a rule like this quietly erodes, and I'd rather have them decided by someone who has watched it happen than by me guessing. 😃
@clasqm: noted, and I'll write it down. If this hasn't earned its place in a year, we retire it without an argument.