It turns out that this Netgate 6100 was set to a "Deprecated Version" branch.
I found this under: System > Update > System Update > Branch
"Latest Stable" wasn't an available branch option, so I changed the branch to the latest stable shown, which was "Previous Stable Version 23.09".
After upgrading to 23.09, I went back to see what branch options were now available. "Current Stable" still wasn't an option, but now I could change to "Previous Stable Version 23.09.1".
Then, after upgrading to 23.09.1, the branch "Current Stable 24.03" became available, so I changed to that branch and upgraded once more.
I think it is a bit silly that I had to change the branch over an over again to finally achieve running the latest stable, but that's what I had to do.
My feedback to pfSense is to add an option to the Branch drop-down-menu that is simply "Current Stable" (without the mention of any particular version number). If you're on a deprecated branch, you shouldn't have to change the branch 3 times in order to finally upgrade to the latest stable.
Upgrading 3 times was understandable, and the granularity to remain on a particular branch/version is also a nice flexibility. Yet, most people would probably appreciate a more generic branch option (like I'm proposing above), so that they can always upgrade to the latest stable version without having to modify branches each time between each upgrade.