Do We Need the Digits of $\pi$?
Are we at best, estimating things when we use formulas involving pi to describe the area, etc. of things?
Not being able to write the exact value of $\pi$ does not mean we do not know it. It has many representations.
The use of $\pi$ in calculations made in engineering, or physics, or other "approximates" is also fine because you know enough digits of $\pi$ to ensure that the error margin is small enough.
No: When we say the area of a circle with radius $r$ is $\pi r^2$, and the circumference is $2 \pi r$, those are exact.
Yes: When we say the area and circumference of a circle with radius $2$ are about $12.56637$, those are approximations.