As of today, the latest version of R (language) is 4.0.3 and the Extra repo supposedly has 4.0.3-1. (I would include a link but I’m not allowed by this site.) However, when I pamac search -a ^r$, or search it in Add/Remove Software, I only see version 4.0.2.
How can I make pamac recognize the latest version?
Update your mirror list and try again.
Use Manjaro - Branch Compare to see where the package is currently available.
Welcome to the forum! 
The 4.0.3 version is currently in Testing and Unstable, while Stable still has 4.0.2. If you really need the latest version today, then you can switch over to the Testing branch, but given the difference between the branches, I would personally simply recommend waiting for the next update to Stable, which won’t be long anymore ─ don’t pin me down on it, but I expect it to be within about a week or so.
Thank you. How can I tell when a version is not in Stable? Here’s the link I got from the Arch wiki: archlinux[dot]org/packages/extra/x86_64/r/