Exercise Related to Frequency Resolution and SNR
Your calculation of the SNR is right and the DFT Bin Resolution is also OK.
One thing you're missing is the effective resolution due to "Windowing" effect.
The DFT of finite number of samples is interpolated by a Dirichlet Kernel (Like Sinc).  It means you resolution is also limited by the main lobe width of the Sinc which is proportional to the inverse of the window length.
Namely, using less samples means wider lobe which reduces the resolution and the ability to differ between two harmonic signals.