Perhaps the following two scientific articles may be of benefit to your search on sleep deprivation and cognition.
1.
Sleep deprivation: Impact on cognitive performance - NCBI - NIH
https://www.ncbi.nlm.nih.gov › articles
by P Alhola · 2007 ·
Visuomotor and verbal functions as well as decision-making have also been assessed. Sleep deprivation effects on cognitive performance depend on the type of task or the modality it occupies (eg, verbal, visual, or auditory).
2.
Effects of sleep deprivation on cognition. - NCBI
https://www.ncbi.nlm.nih.gov › pubmed
by WD Killgore · 2010 ·
Effects of sleep deprivation on cognition. Killgore WD(1). Author information: (1) Neuroimaging Center, McLean Hospital, Harvard Medical School, Belmont ...
It looks like the previous answers focused on cognition, not meta-cognition.
The mindfulness research involving sleep is mostly about treating sleep difficulties, but I found this paper on emotion regulation ability when sleep deprived - Article Poorer sleep quality is associated with lower emotion-regula...
There have been many studies on sleep deprivation and cognitive function. I see that several people have suggested specific studies on this topic. I am attaching a study by Halbach et al. (2003) that should really get our attention as it has to do with medical residents and how sleep deprivation impaired their cognitive abilities. Take a look at it and if you are interested, I will be happy to send you more.
One thing to keep in mind is that REM sleep, in particular, seems to play a role in memory consolidation. So, you may want to narrow down your search and look at studies on REM deprivation and cognitive function.