RPGs come immediately to mind. Your partner in Disco Elysium is more competent than the main character for reasons that will be immediately obvious. Bethesda's RPGs are also open world, and while you'll start out alone in them, you get permanent companions pretty quick (especially if you know where to look). They also get more chatty in the world and more character development in the later games. Fallout 4 more so than Skyrim more so than Fallout 3, for example. Starfield makes you swap them out if you do the main story, which I don't know if you'll like or not.
For a dedicated shooter, I think Titanfall 2 has the most protective companion I've seen in the genre. Get this one on sale, since it has its robust multiplayer priced in, but it has an excellent--if a bit short--single-player campaign.