I don't know, and this is not my area, but John Aziz is pretty sure that it's a myth under current circumstances. Hopefully I understand his argument. He uses as evidence this chart:
I'm not sure what data we're looking at here, but I assume its definition of Available Labor Supply is something like the CPS workforce definition. Aziz's argument makes a lot of sense in a representative agent or homogenous agent world. If there are 100 job applicants, and there are 50 job openings, then obviously none of the unemployment is voluntary because the job market wouldn't absorb any new job applicants even if they tried. This depends a bit on semantics, but it's good enough for me, to a first approximation.
But consider a model with two types of skillsets, carpentry and blogging. Suppose there are 50 people who count as unemployed (they are "seeking work"): 25 carpenters and 25 bloggers. Now suppose there are 45 job openings. By Aziz's logic, there is no voluntary unemployment. Now I tell you that 25 of the job openings are for carpenters, but only 20 of the carpenters are applying for those jobs while the other 5 carpenters are just "talking to friends about job opportunities" so they count as unemployed people. So it's possible that 5 carpenters are voluntarily unemployed (in anything but a semantic debate). And this argument can extend to geographic heterogeneity or anything else; it's pretty hard to pin down how much it matters.
Is this kind of mismatch happening now? I don't know, but if there is evidence that reservation wages are high or job-search intensity is low, I don't think we can rule it out. If you acknowledge heterogeneity and admit that transfers affect incentives to search for jobs (or start businesses), then I don't think you can be as confident as Aziz. We at least need more evidence about mismatch and other things.
The broader point is that too much aggregation can get you into trouble with some questions. Simply knowing aggregate numbers for job seeking and openings doesn't tell us all we need, since we don't know how many potential openings exist for every kind of worker. Further, we should keep in mind possible general equilibrium effects; what would happen to wages or entrpereneurship if people had a smaller safety net, and how would that affect labor demand? Again, this chart doesn't tell us.
I'm certainly not suggesting that transfers are the dominant driver of the current employment situation, but I think Aziz goes too far in suggesting that there's no involuntary unemployment out there.