Create a Magic Makeup Mirror with Pose Detection -- Episode 559

You could perhaps add a LED ring around the HyperPixel display to help throw some light onto your face to help the camera. (Bonus points if you can style it as a theatre style green room mirror with round LEDs that pop out when you open the compact ) Just don't overdo the candelas otherwise you will be blinded in the process.

You could also try a ring of white pixels on the display itself but probably not enough light to make much of a difference.

Arducam have some R-Pi compatible ultra low light cameras (IMX462 Starvis sensor) which might be worth a look at, although may be a bit large for a final compact mirror.

https://www.arducam.com/product/arducam-for-raspberry-pi-ultra-low-light-camera-1080p-hd-wide-angle-pivariety-camera-module-based-on-1-2-7inch-2mp-starvis-sensor-imx462-compatible-with-raspberry-pi-isp-and-gstreamer-plugin/  

So a smaller less sensitive camera sensor with the LED light ring illuminator might still work out better (and cheaper).

I've got one of their IMX291 2MP cameras in a USB webcam format which has quite good low light performance. Sometimes 'less is more'.

It is UVC compliant but the downside is that without a OEM driver, not all the camera properties are accessible from standard USB camera applications. You either have to use the likes of AMCap or equivalent to access the camera pins or alternatively set their properties using OpenCV, which is something I need to look further into but looks doable according to this:

https://docs.opencv.org/3.4/d4/d15/group__videoio__flags__base.html#gaeb8dd9c89c10a5c63c139bf7c4f5704d

I like the arducam cameras. I had one that had such a bigger field of view than a raspberry pi camera. 

They have recently added a 64MP R-Pi compatible camera with autofocus lens  to their range.

They have recently added a 64MP R-Pi compatible camera with autofocus lens  to their range.