My interpretation of this is that the muon measured radius of the proton is the correct one. This rules out the speculation that the muon measurement was accessing some sort of new physics which caused it to be 4% off. The key quote is here:
"Some researchers speculated that perhaps some previously unknown physics could make muons act differently than electrons. This would have required a revision of the standard model of particle physics, which predicts that muons and electrons should be identical in every way except for their masses — and might have pointed to the existence of yet-to-be-discovered elementary particles."
This is the reason for this precision research: it could give you the hint for where to look for new physics. This
result, far from "deepening the proton-size puzzle", says that muons do not have any new physics. In other words, it's a null result.
"Some researchers speculated that perhaps some previously unknown physics could make muons act differently than electrons. This would have required a revision of the standard model of particle physics, which predicts that muons and electrons should be identical in every way except for their masses — and might have pointed to the existence of yet-to-be-discovered elementary particles."
This is the reason for this precision research: it could give you the hint for where to look for new physics. This result, far from "deepening the proton-size puzzle", says that muons do not have any new physics. In other words, it's a null result.