I just spent the last 20 minutes rummaging through my house, trying to find a pack of Tapo outlets, since I bought a massive number of their outlets, switches, etc to fully upgrade my parents’ house (they spend what feels like half their time just running around switching various lights and plug-in floor lamps on and off).
I could have sworn I had kept one pack at home, specifically so I could do a trial-run here first, but, if it is here, it seems to be exceptionally good at hiding. Probably doesn’t help that my place is currently a complete mess… 
Sorry I couldn’t be of help, but I’ll take another look around later today; if I do come across them, I’ll be sure to take measurements and post the dimensions/some pics for you.
EDIT:
I checked their site really quick, which managed to be singularly unhelpful, as, according to their specs, it is entirely two-dimensional:
“Product Dimensions (L x W x H)
128.7 × 84.7 mm”
I did manage to find a review of them, though, and, while they similarly seem to believe in their two-dimensionality in reporting the size, they did include a picture of it hanging out of what appeared to be an old-style metal outlet box - definitely looks pretty snug, but, depending on how much of a rats’ nest of wiring it will have to share space with, should be able to fit? Anyway, here’s the link:
EDIT 2:
The measurements given by TP-Link seem to just be the external dimensions with faceplate - did find this in the manual, though, for whatever it’s worth:
“Install only in a suitable UL Listed outlet box (suitable dimensions:
H > 2.95 in./75 mm, W >1.81 in./46 mm, D > 3.15 in./80 mm).”
Here’s the full manual, for reference:
https://manuals.plus/tp-link/tapo-p210m-smart-wi-fi-outlet-energy-monitoring-manual