How many digits of Pi did the old Egyptians know?

From "Rhind Papyrus" from 1600 BC we know that the Egyptians had an estimate for $\pi$, namely 3.16, meaning they knew only 2 digits of $\pi$. According to this article they knew more digits, at least 4 digits of $\pi$. Around 200 BC Archimedes estimated pi to 22/7 which is 3 digits of $\pi$. This indicates that the Egyptians knew more digits 2000 years before Archimedes, however, it's not clear to me how many digits they actually knew.

The article does not say what you think it does. The article hypothesizes that the ancient Egyptians used a trundle wheel to accurately measure distance. An estimate of pi is not needed to make an accurate trundle wheel. What's needed is an accurate measure of the circumference. There's no reason to measure the diameter, which is harder to measure accurately than is the circumference. Furthermore the circumference will not be given by $\pi\cdot d$ if the wheel isn't perfectly round.
Ancient Egyptians estimated the area of a diameter-$d$ circle as that of a side-$8d/9$ square. This is equivalent to $\pi\approx\frac{256}{81}\approx 3.16$. This means they were wrong in the second DP, and wouldn't even truncate to 1DP accurately, as they'd round up to $3.2$ (not that they used base $10$ like that). Even by the standards of the ancient world, it's a quite inaccurate estimate of $\pi$ (although better than the Biblical $\pi\approx 3$). However, it gives what seems to be the only ancient rational approximation of the fourth root of $\pi$ (namely as $4/3$, and this is indeed its first convergent).