That's just a bad name. This is essentially a nonrandomized unblinded controlled trial using representative sampling. Only two steps below a full RCT unless you suspect foul play.

I'm not sure how you'd blind lack of sleep and that's not the point, so the only issue is lack of randomization.

Much better than an observational study.

Quasi-experiment is not necessarily a bad thing. It is to denote a study that does not have a traditional control-experiment structure with explicit pre- and post-measurements. This is particularly difficult to do with real time data analysis over time periods or with concepts that have ill-defined units of measurement.

For example, productivity and learning would be considered ill-defined. How can you prove more sleep makes you more productive? Since that is difficult, you can instead do a quasi-experiment or case study to observe the effects.