Monitoring the time evolution of the intensity of the Covid-19 pandemic within the pandemic and despite the limited quality of the data is both crucial and challenging. In the context of a pandemic, providing a level of confidence in the estimation of epidemiological indicators is essential to inform decision makers. The present work proposes a Bayesian estimation of the pandemic Covid-19 reproduction number and of the denoised reported counts through credibility intervals. The challenge stems from an epidemiological Bayesian model robust to errors in reported counts, which yields a non differentiable a posteriori log-density. Four different Hastings-Metropolis algorithms combining Langevin approaches and proximal operators are compared on a toy example; the most efficient one is plugged into a Metropolis-within-Gibbs algorithm performing a credibility intervals-based estimation of Covid-19 pandemic indicators, exemplified for several countries worldwide.