One may feel that their job is not making a meaningful contribution. That doesn't translate to the job being useless or BS.
Did you read Graeber's book? I have seen a lot of the mechanics described in every job I've ever done, including roles like the Box Ticker or the Flunkie - or whatever he calls the "entourage" people, it's been a minute. These types of functions exist and often don't contribute to the product, company growth or financial success. That's what bullshit means in context: busywork, economically non-functional. Now, not every compliance role (Box Ticker) is a bullshit job. Nor is every assistant (Flunkie). But enough are for the pattern to exist and Graeber to have a point.
Markets and companies, which are often assumed to be efficient, are remarkably tolerant to inefficiency in their internal politics and bureaucracies. There is also a degree to which large enough companies can just coast on prior success before they feel the impact of bad process or ill focus and start to feel they're bleeding money.
Looking at the broader economy, there are a lot of "lifestyle" products that squarely fall in the category of luxuries. There's "consultancy" that exists to play politics in companies and doesn't do anything, like SAfE/Agile/Scrum/transformation consultants (not all, but enough), management strategy consultants, etc. This is where the Economist's alienation comes in: there is no meaning to contribute to when working at one of these companies, as they offer and stimulate pure consumerism, or political faire semblant (=pretending) as a service.
My conclusion is both Graeber and the Economist are right: the left Venn diagram contains actual useless jobs (as in, don't contribute to the process). The right diagram contains a lot of meaningless jobs where the product/service is ephemeral or purely materialistic, leading to alienation. The two diagrams overlap.
As to whether 70% of jobs are contained in the union of the two? Perhaps not, but I think it's a big enough problem for it to lead to an increase in burnouts, boreouts, depression and suicide.
Perhaps you have a perception of a certain kind of individual tenure associated with government jobs ("it's so hard to fire them"). That perception might even be true, though it's a little debatable since there are some fairly legitimate reasons why these rules exist.
But even if it is true, that doesn't mean that government work over the long haul is secure.
Given the motivation, "waste" has a narrow definition in the private sector: anything that doesn't contribute to the baseline. Non-waste can take many forms, e.g. improving product quality, reducing costs, managing brand perception, market research or regulatory capture. There is wiggle room for subjective assessment, like when companies see IT not as a catalyst but a cost centre and therefore fundamentally waste.
The government has a different motivator entirely: the greater good. Waste and inefficiency take on another meaning in that context. Digging and filling ditches isn't wasteful if it ensures people have an income. In a government context, it's a useful job because it achieves stated goals, but still a meaningless one.
The wars on terror and drugs are examples where it becomes more murky. For some, they are both useful and meaningful. For others, they're just one or perhaps neither.
There are also government projects that seem like waste at the time but turn out to have tremendous value and even be private sector useful today. Examples are legion in military inventions that later became staples, such as microwave ovens, the Internet, cell phones. Regardless of how you feel about landing on the moon and NASA in general, we have now have non-stick pans, GPS and solar panels.
In summary: looking at government through the lens of the private sector is failing to understand a simple truth: corporations are individualistic, where governments are collectivist even in a capitalist system.
I don't want to advocate for this idea necessarily, just that I think the "bullshit jobs thesis" might mean something different to different people. The Economist article closes with an admission that "part of Mr Graeber’s thesis turns out to be correct," discussing the adage that "people leave bad managers, not bad jobs." Many variants of the bullshit jobs thesis I think propose an increase in bad managers, who are part of a larger unnecessary management structure.
I guess overall I felt as if the Economist piece was missing a few things.
Personally I'm fairly sure there's a large number of "bullshit jobs" and I have my own, unfounded, opinions regarding which jobs that might be. I'm just not convinced that we can identify these jobs by asking those who work in those position.
There's also the jobs that truly are essential, but only because something somewhere else is broken.
https://en.m.wikipedia.org/wiki/Corruption_Perceptions_Index