How to calculate power of a signal at one specific frequency?
Ultimately if your noise is white then the matched filter would be the best approach (multiply by one frequency and sum-- if it is complex you would multiply by the complex conjugate- both a form of correlation). This is equivalent to computing a single bin in the DFT (assuming your frequency is on bin center, otherwise equivalently the operations in the DFT can be modified to be centered on your particular frequency). This approach has bandwidth which for white noise will have the equivalent power of a similar brickwall filter with a bandwidth of $1/T$ where $T$ is the duration of your correlation; but importantly the frequency response is a Sinc function (or Dirichlet Kernel if discrete as a sampled Sinc) in frequency which means this approach is sensitive to non-white noise at other frequency locations (a strong tone very relatively far away would show up in your power measurement); the main lobes of the Sinc only roll-off at 6 dB per octave in frequency.  So for white noise, this approach is optimum, for other applications with colored noise, applying a properly designed filter to the signal to attenuate &quot;out of band&quot; noise before measuring the power would be recommended.
For measuring a single tone with the equivalent of a single DFT bin, the Goertzel is a well known choice that is efficient at doing this very thing.