text: Title: Tuning `alpha` in `GaussianProcessRegressor`
  Body: ### Describe the workflow you want to enable
  
  In the [GaussianProcessRegressor](https://scikit-learn.org/stable/modules/generated/sklearn.gaussian_process.GaussianProcessRegressor.html), `alpha` stands for the likelihood variance of the targets given the inputs: $Y = f(X) + \sqrt{\alpha}\xi$, where $f(X)$ is the GP and $\xi\sim N(\cdot|0, I)$. It is an important hyper-parameter, as it represents the measurement error in the target labels.
  
  Currently, the `fit` does not tune $\alpha$. It only tunes the parameters of the kernel. 
  
  ### Describe your proposed solution
  
  Would it be possible to enable the tuning of $\alpha$ when calling `fit`?
  
  ### Describe alternatives you've considered, if relevant
  
  Note: one could try to work around the problem by adding `WhiteKernel`, but this is not equivalent to tuning $\alpha$ and retains a different interpretation - see [here](https://gaussianprocess.org/gpml/chapters/RW.pdf), eq. (2.25) and (2.26). Here, $\sigma_n^2$ plays the role of $\alpha$.
  
  ### Additional context
  
  _No response_