I was watching Better Call Saul the other night (Season 5, Episode 9, to be precise), and the character Kim Wexler exclaimed to Lalo Salamanca: “That‘s what you’re on about?”
I covered the expression “to be on about” something in 2013; it’s kind of the British equivalent to the American “going on and on about.” The problem with Kim’s use of it is that Better Call Saul is a prequel to Breaking Bad, with the current season taking place in 2004, and “on about” didn’t really take hold on these shores till after that. This chart from Google Ngrams Viewer gives a bit of a sense of the timeline:
I say “a bit” because both the British and American timelines overstate the use of the phrase, as a result of examples like a record review saying of a musician, “he’s on a lot about ten of the tracks.” My conclusion is that the NOOB “on about” was close to nonexistent in the U.S. in 2004, and would not have been used by a New Mexico lawyer with no apparent obsession with English television or novels.
At about the same time, I was talking with a University of Delaware colleague, Ann Manser, who said she was watching an actual English TV show, Lovejoy (Season 1, episode 9, “Death and [sic] Venice”), and was taken aback to hear an American character say “catch him up.”
That actually took me aback because I wasn’t familiar with the expression, which, Ann explained, is the equivalent of our “catch up to him.” (We do have a “catch [someone] up,” but it’s different. If a kid has missed school, the teacher might ask another student to “catch her up on what she missed.”) Ann said she and her husband thought the phrase was some sort of clue, maybe that the supposed American wasn’t really American after all. But no, there was no follow-up. You might call it, “The Case of the Shoddy Teleplay.”
notoneoffbritishisms.com 
In British English, ‘that’s what you’re on about’ probably means something like ‘I have realised what you are trying to say, even though you’re not saying it very well’. Is that how Kim meant it?
It’s a very common expression, and different to ‘going on about’, which, as you say, is similar to ‘going on and on about’, but not quite the same in either quantity (or quality).
There are loads of pretend Americans in British TV shows. But then again, I see loads of pretend Americans (Brits) in US TV shows (and films). I am even noticing more and more American actors playing English characters in British TV shows and films.
I suspect the fake american was Alexander Knox, born in Ontario.
I know “catch me up” mainly because of a children’s book I used to read my kids. I don’t recall what the book was, and a Google search hasn’t helped, but it featured a recurring line of something like, “…they never could catch him up.” That alerted me to the phrase and, sure enough, I heard it fairly often among British English speakers.
I’ve certainly heard “… catch him up.” in British English but only to physically catch up with someone. Not familiar with helping someone catch up with their work or studies.
For instance, in a race or a chase.
It seems to be an Americanism, then.
When I updated my details on paypal.CO.UK , I was told that I “was all caught up”. Is that a normal US usage?
Yes.
Anachronistic language in movies and television is such a distraction, and it’s not even on producers’ list of things to watch out for. James Cameron boasted about how even the buttons were matched to the period, but the script was pure 1990s Americana. For instance. Turn on any purported period piece to see similar.
James Cameron being the producer of the last Titanic movie.
Catch him up doesn’t sound at all odd or out of place to me. I have lived in the western US all but two years of my life (the other two I spent in the southern US). Catch (someone) up could mean that they are behind on their studies as has been suggested or could mean that the person missed something due to being absent. It might also be used in frustration to imply that the person is mentally slow or hasn’t been paying attention which is how I think it was used in Breaking Bad. As in – I don’t have the time or the patience to hold this idiot’s hand and walk him through the details until he understands things so I’ll delegate that to you – catch him up will ya?
Sorry, Better Call Saul, not Breaking Bad.