How is signal to noise ratio actually measured by receiver equipment? This sounds like quite a basic question but it surprised me, how is SNR actually measured?
You have the incoming signal:

It seems like the SNR is just the visual comparison of the peak signal 'amplitude' to the noise 'amplitude'. In this case the signal 'amplitude' clearly includes noise as well, because it is summed together i.e. it is the sum of the noise 'amplitude' at that frequency and the signal 'amplitude' at that frequency because 'amplitude' in this case referring to volt-seconds under the curve of a complex sinusoid at that frequency times the signal (which contains the noise sinusoid and signal sinusoid at that frequency, which creates a greater amplitude sinusoid at that frequency and therefore there is more area (volt-seconds) under the curve when that sinusoid is multiplied by a complex sinusoid of the same frequency.
I'm assuming the received signal power would be calculated by squaring the $V_{RMS}$ of the samples taken and I assume noise is also sampled at a separate occasion to get the $N_{RMS}$ (or so called noise variance, but real noise doesn't have a 0 mean i.e. no 0 frequency component), or it uses a frequency spectrum analyser or something to get the voltseconds at unused frequencies and then integrate it with respect to frequency i.e. $s^{-1}$ to get the average voltage and then square it to get the average power, the problem with that being that you can't measure the noise on the frequencies that are used, so I would think that it is acquired separately, like in the wifi layer 1 preamble and training sequences.
But the signal comes in as the signal+noise, so surely it's actually (signal (${V_{RMS}}^2$ + noise ${V_{RMS}}^2$) / noise ${V_{RMS}}^2$) that is being measured, unless noise is deliberately subtracted from the signal i.e. received signal (${V_{RMS}}^2$ - noise ${V_{RMS}}^2$) / noise ${V_{RMS}}^2$ to get the SNR? I'm assuming that the traditional $P_{\text{signal}}$ means the signal without the noise and not the received signal as it is seen.
The SNR is simply the mean-square of a demodulated symbol divided by the variance of the signal, or in dB:
$$\DeclareMathOperator{\SNR}{SNR}\SNR =10\log_{10}(\mu^2/\sigma^2)$$
$$=20\log_{10}(\mu/\sigma)$$
A typical metric for this in receiver equipment is the Error Vector Magnitude (EVM) where an &quot;error vector&quot; is the Euclidean distance from the actual sample at the optimum timing location in each symbol to the actual symbol location in a reference waveform (as the distance to closest decision boundary, just prior to decision). EVM is the normalized rms of the error vectors over multiple samples, where the waveform and the decision boundaries are scaled to either the rms amplitude or a maximum amplitude in the constellation, depending on which standard is used. We can therefore use one sample for every symbol to compute a sufficient number of errors to derive a statistical quantity.

See this post for more details on computing EVM from which the above graphic was copied: How to calculate EVM in %age of an Equalized Constellation in 16QAM?, but to describe it simply we statistically estimate with enough samples the standard deviation of this normalized error. The EVM is the average of the noise magnitudes as a percentage of the normalized constellation which represents the signal. (The average of the magnitudes is not the same as the magnitude of the average ($\mu$) so an additional small adjustment factor for this is needed in translating EVM to SNR that depends on the signal constellation used and the normalization that was used for computing EVM).
The relationship between EVM and SNR is therefore:
$$\SNR =  20\log_{10}(1/\text{EVM}) - K$$
Where $K$ is an adjustment factor depending on the peak-to-average of the constellation and how the constellation was normalized to the peak for computing EVM.
This would be affected by the portion of the noise as in the OP's figure that is within the bandwidth of the receiver after demodulation just prior to symbol decision (which is the noise bandwidth we are concerned with: the waveform bandwidth).