I had not noticed this question previously, this was an area I was working in some years back. In fact the Noise Figure varies quite a lot with set up conditions and FDA chosen. have not working on this for awhile, but here is what I could find - this one gives you most of what you want for an FDA NF calculation - somewhere I have my original hand calculations and associated spreadsheets, not looking for it further right now.
The really cool thing about a matched input Z single to diff design is you can do that with only a single input resistor which will give the lowest NF - I call that the active balun configuration. Equation 9 here gives you the NF for that configuration (which then requires a very specific Rf value) Not sure if I ever got the NF with an Rt included, pretty sure I did, but not finding it yet. A lot of the active balun work was intended for AC coupled inputs to a single supply FDA.
https://www.edn.com/wideband-fully-differential-amplifier-noise-improved-using-active-match/
