I think you may well need to give us a little more to go on.
At first glance these are two different things that don’t really overlap ( as you have generally to be employed to benefit from an EAP so can’t see link to the unemployed).
I still can’t see a link between the two topics. So I maybe missing the point.
On unemployment. I think there is an interesting story. We all expected the situation to be much worse. Many were predicting the end of furlough to see mass unemployment. But the situation so far has been very much more nuanced.
Added to that the impact of Brexit. And we actually see record numbers of job vacancies and the unemployment levels no where near where expected. Indeed the government job placement schemes are running at much lower volumes than expected.
Additional factors are the changes in some peoples work /life choices. Some people who tried things out in lockdown/ furlough not going back to their original professions. Burnout in some professions. Changes in priorities leading to the “great resignation” etc etc.
It’s an interesting area and a position few people 18 months ago expected us to be in.
Not sure what you are looking for on EAPs. Certainly take up has been higher but not sure this is a structural change but more possibly a temporary one.