I have the same setup; R + adapter + EF 70-300 IS II. Same problem.
Solution: Use AI-Servo.
Problem only occurs in Single shot (or potentially BBF shooters). However, with the EOS R's knack of nailing things, even in AI-Servo, and especially with this lens, peak sharpness is not an issue with AI-Servo.
This has been an issue with this lens since the 80D. When operating this lens in DPAF on either an EOS M, or now EOS R, there is something finicky about nano-USM lenses which causes them to erroneously report a shooting distance not possible (IE false positive that you're beyond macro distance). This occurs on both the 70-300 IS II and EF-S 18-135 IS USM. I've witnessed the latter on an 80D in live view.
It doesn't happen all the time, but plenty in my observation. Enough to be notable.
It never happens in AI-Servo as the lens will continue to drive searching for a phase shift instead of "giving up". Always nails it without issue when in AI-Servo.
It did not occur on my former EF 70-300 DO adapter nor on any other lenses.
Hope that helps explain the phenomena, confirm it's there, how it behaves and what you can do about it.
Canon should firmware fix that though. Probably a lens firmware if I had to guess as those lenses have CPU logic in them. It doesn't happen on other lenses, hence that conclusion.