As per the 2019 redefinition of the SI base units, the molar gas constant is exactly
The wikipedia number comes from the full multiplication of the Boltzmann constant, $k_B$, and the Avogadro constant, $N_A$, both numbers defined as having no uncertainty due to the aforementioned recent changes to the SI. I don't know why your link hasn't updated their website but you can click the actual symbol of the molar gas constant on the website you linked to check that it is, indeed, derived from the two other constants I mentioned.
You can then use a full precision calculator to verify the number yourself. Note that Google's calculator does not show you the full decimal value, but other online calculators will. For most calculations, however, these last few digits aren't going to affect anything much at all. Other constants similarly can be found on the Wikipedia page I linked above.