Bush II had maybe a 1.5% drop in the participation rate; after 2009, the slope steepened so Obama had a 3-3.5% drop.

A reduction in the participation rate often disguises a rise in the unemployment rate. It can be because of retirement, education, etc., but it can also just signal discouraged workers. People get bent out of shape mistakenly thinking that if unemployment benefits expire you're no longer counted as unemployed, so the unemployment rate is artificially low (benefits and unemployed are different things); if you're a discouraged worker and don't look for work, you're not included in among the unemployed and it really does make the unemployment rate artificially low.

As for current stats, I take them with a grain of salt. When NYC has mandated that a large portion of its workforce be unemployed it's not the same as the kinds of structural things that lead to higher unemployment during a normal recession. Government enforced unemployment has to follow different rules. When the government mandates unemployment, of course it's going to be higher--it's like reduced air pollution with an EPA mandate or increased compliance with safety belts when cops are out in force. During a pandemic, a lot of people that might seek work won't if they're afraid given the 99% fatality rate and the horrors that accrues to each COVID patient (because they're subject not to be put on a ventilator but to ventilating); that's not "discourage" but "terrified". COVID-19 bears real risks, but the media's profited from stoking terrah here just as it did in 2004 and 2005. All the economic definitions made assumptions about cause and effect, and now the cause is different and we're ignoring the assumptions. It's sloppy thinking.