Ok great, the servo mode should rule out movement. One other thing, is your firmware up to date? That's going to make a huge difference too. Especially with adapters involved. I believe you might be having the same problem that I had recently. I was at a park & couldn't pull focus on a bird. I was shooting it slightly backlit, essentially in similar lighting to your photos. I took a deep dive on how focus works with these cameras. What I found was that there wasn't enough contrast for the camera to grab focus on. This was despite it appearing that way, but I manually focused & took a few shots. Upon review of those, I could see why there was an issue. The dim light just didn't create anything sharp to lock onto. Since it was midday, the infrared focus aid couldn't fire either. Even if it did, the dusk sunlight would have canceled out most of it. Going by what your focus is locked on to, I think this might be your issue as well. Which is why I recommended testing using the method described above. This way you can check k to see if it was just a contrast issue due to a combination of lighting & focus selection.
One other important thing to remember is the dual pixel auto focus on your camera may not work on an older lens. This feature gives you a great edge when it comes to focusing in these situations. It's another benefit of the RF lens system. I also did look up using the auto eye focus feature, which it appears you might be using. According to a bunch of online info, the older EF 50mm doesn't work great with the eye tracking feature. It's very slow & tends to hunt a lot. So if you are pushing the shutter button quickly, you may be getting focus just in front or behind the subject. Especially if it begins hunting. This is particularly true in low light, where it may not lock at all or continue to hunt. Your camera does have a feature where you can tell it to shoot within a certain percentage of focus lock. I don't believe it's usually 100% focus. There's a tiny bit of wiggle room, & at the aperture you're using, that would easily result in your focal plane being off. If you'd like more info, try asking chatGPT "how well does the Canon eos R work with a Canon EF adapter & nifty 50mm lens when using auto eye focus." It will give you the run down. To fix this, you might consider shooting on spot mode for concise focus without issues. I personally don't have great luck with the eye tracking myself. I use spot mode. Be sure to turn off servo mode so you can lock focus & then adjust your composition.
As for the setting you requested, I dont have my camera handy, but I looked it up. Try turning this on or off & see what works best. I believe default is on. Some people claim it works better off. So try both & see what you think. It might be situation dependent as well as affected by the lens you're using.
Menu → Custom Functions II: Autofocus (C.Fn II) → Item 4: "Lens drive when AF impossible"
Set it to 0: Continue focus search to enable hunting through the focus range when no subject is detected.
Set it to 1: Stop focus search to prevent the lens from hunting and conserve battery.
