RX antenna is connected to the Spectrum Analyzer whose reading is regarded as P_RX. TX antenna is connected to a transceiver module that is set to work at the target frequency and emit certain power (P_TX). Question: Can I deduct S21 from P_TX-P_RX?
Yes, you can deduce an S21 (forward gain) from that by dividing P_RX / P_TX but I think that that number would not mean very much.
Move the RX and TX further apart: that S21 will change
Move the TX antenna (assuming non-isotropic radiation pattern): that S21 will change
Move the RX antenna (assuming non-isotropic radiation pattern): that S21 will change
Stand in between RX and TX: that S21 will change
Place something conductive between RX and TX: that S21 will change
So I do not see how the S21 you'd get would mean anything at all. It would be the S21 under those circumstances. I fail to see how that number can be useful in any way.
You can perform a measurement of scalar S21 (power gain only) using Spectrum analyzer on the medium (antenna + free space + conductor).
You won't have good accuracy on the phase information compared to VNA.
People do use SA + SG for S21 measurements especially if they want to get the channel matrix over a long distance.
In that case, to ensure a good phase accuracy, one has to use a GPS clock for synchronization, over the two remote Tx and Rx.