Honestly I don't see that many typos in other papers; grammatical issues, sure. But it would appear that not knowing what the squiggly red underlined words are is a requirement of being a Graun writer or editor.
It is true they were notorious. Sufficiently so for it to be the standing joke of their name in Private Eye. It is also true that probably, some of the time, it was in-crowd joking.
I have a deep antipathy to Murdoch press, having said that they used to have remarkably high editorial standards in the Australian flagship newspaper (called "The Australian") and when News Ltd went on a cost cutting drive, around the time of the collapse of their main competitor, Fairfax Ltd (caused by Warwick fairfax, who basically wrecked the empire: he now consults in the USA on .. how to be a successful entrepreneur!) It merged a huge amount of sub-editor functions into a JV with Fairfax, which subsequently basically failed in-place: They sacked the good staff, and kept an out-source agency which had no clue. The Oz, is now pretty U/S for basic grammar AND spelling.
They also routinely now do pun leads. This was funny for about half a second, ever. The Graun also does far too many pun leads. I think all newspapers wind up there.
A good fictional account of news headlines and the journalistic pressures of newspaper writing in happier days is in "leaven of malice" by Robertson Davies: a fictional Canadian newspaper, beset by a cruel trick played in "hatches, matches and dispatches" -"The Shipping News" has its moments too.
Probably worth taking into account their line in that article about how good they are at fast-turnaround journalism. Typos are always going to happen in that environment I’d guess.
3. I still regularly see trivial grammar errors (repeated words, etc) in opinion pieces on the Guardian, not just breaking news and liveblogs. I guess some of those opinions pieces might be treated as "fast-turnaround journalism", AKA "hot takes". The rate of simple typos there makes me wonder about more important things like factual accuracy.
Edit to add: reading the article more closely, it sounds like they've only started using this new system quite recently, so hopefully it will help them improve. I stand by my opinion that in recent years the rate of typos and grammar errors has been higher on the Guardian than most other comparable news sites.
It's worth noting that Typerighter doesn't include a dictionary yet – it only helps our journalists with style-guide related errors. A dictionary is on the roadmap, though.