Increasing SNR and Dynamic Range using Oversampling
OP clarified that the question in the comments as follows:

If we ignore any modulation for now and assume that we are receiving
pure tones plus the band limited noise and we try to improve the SNR
in post processing how much improvement can we expect by oversampling
and is there a limit to it? My original question was about this
aspect.

First consider the case of sampled white noise (no band-limiting of the sampled signal other than anti-alias filtering prior to the A/D converter), the improvement in SNR due to oversampling a pure tone would be the processing gain in a matched filter such as a correlator to $e^{j\omega n}$ given as $\sum x[n]e^{-j\omega n}$:
$$PG = 10\log_{10}(N) \text{ dB}$$
This is because as we sum the samples in the correlation process, the signal component of each sample which is correlated from sample to sample will increase at $20\log(N)$ dB while the noise components will increase at $10\log(N)$ dB: The total signal magnitude would be $x_1+x_2+x_3 +\ldots$ while the total noise rms magnitude would be $\sqrt{x_1^2+x_2^2 + x_3^2 + \ldots}$
But with band-limiting, as we increase the sampling rate beyond the Nyquist frequency for the bandwidth of the signal, there will be no further increase in SNR: since the signal is bandlimited (no longer white), adjacent samples will be correlated both in signal and in noise, and as we sum the samples in an attempt to increase SNR, both the signal and noise components of the signal will increase at the same rate ($20\log_{10}(N)$).
Assuming a constant noise out to $f_b$ and then rolling off after that, we would increase SNR after correlation up to the point where $f_s/2 = f_b$ (for a real signal) Increasing the sampling rate beyond that will not increase SNR. Further we have a practical limit for long averaging situations from ADC spurious free dynamic range (SFDR), phase noise from clocks and local oscillators, and similar $1/f$ noise sources where the signal is no longer stationary and increasing the averaging duration further will begin to degrade SNR.  The Allan Deviation (ADEV) is an excellent statistical tool for determining the optimum duration to average given we have no other constraints on the time interval. (For more on ADEV for this application see What determines the accuracy of the phase result in a DFT bin? )

If the input signal has a fixed analog bandwidth, and you are properly not limited by the quantization noise, and front-end filtering has been sufficient to not have aliasing to occur, then oversampling will not have any effect on the SNR in band.
The idea of oversampling is to spread the quantization noise out so that it is no longer swamping out the noise floor of your signal which should be the limiting factor to SNR, and to allow for appropriate filter design to eliminate noise out of band from folding in at a lower sampling rate. These are the two most prominent reasons to oversample: increasing the effective resolution by spreading out the same total quantization noise over the full sampling bandwidth, and increasing the total frequency space in which we can do digital radio processing of signals outside our primary band of interest, for filter rejection and multi-carrier operations. For more details on the first and it's limitations please see:  What are advantages of having higher sampling rate of a signal?
It is assumed that the proper receiver design will filter out all noise that is outside of your signal bandwidth (the matched filter), so given you are sampling sufficiently high according to Nyquist (2x the bandwidth, plus some margin for realistic filter realization) then there is no reason to sample any higher once the signal is properly filtered (and this only increases power dissipation, increased resources, etc).
The strategy should be to sample sufficiently high at the front-end of the digital receiver for the filter designs involved and in consideration with the analog filtering that may be done for anti-aliasing, then once out of band noise, interference and other channels are filtered out, reduce the sampling rate to be as small as possible (typically 2 samples/symbol).
This may add a further intuitive explanation: Consider a band-limited random noise process with the sampled time domain signal shown below along with a histogram of those samples along the right axis, and then immediately below that is the spectrum. As long as we sample that spectrum more than twice the bandwidth shown, no matter how much faster we sample we will still get the same histogram, from which we get the standard deviation of that noise.
If we had additional noise energy outside the signal's bandwidth, then oversampling can of course help us to eliminate that interference through filtering where it could otherwise fold into band with a lower sampling rate-- but this isn't improving SNR by oversampling, this would be implementing proper receiver design by filtering out interference (which that task alone may require a higher sampling rate).