What are the algorithms used in ssm.estimate and bssm.estimate for calculating standard and bayesian state-space solutions?

In the Matlab documentation of ssm.estimate, you put this reference:

[1] Durbin J., and S. J. Koopman. Time Series Analysis by State Space Methods. 2nd ed. Oxford: Oxford University Press, 2012.

But in the documentation of bssm.estimate, you put these two very old references:

[1] Hastings, Wilfred K. "Monte Carlo Sampling Methods Using Markov Chains and Their Applications." Biometrika 57 (April 1970): 97–109. https://doi.org/10.1093/biomet/57.1.97.

[2] Metropolis, Nicholas, Rosenbluth, Arianna. W., Rosenbluth, Marshall. N., Teller, Augusta. H., and Teller, Edward. "Equation of State Calculations by Fast Computing Machines." The Journal of Chemical Physics 21 (June 1953): 1087–92. https://doi.org/10.1063/1.1699114.

I saw that the Durbin's book also deals with the bayesian case, but it is not clear if you used this book for both ssm and bssm implementations. Please, could you clarify this? Why? Because I am writing a paper with novel algorithms for solving state-space models and tested the simulations with my algorithms and these Matlab R2022a's functions. So, I need to provide some details about the methods used in Matlab's functions.

Thanks,

Jose