Let $k$ be a field. Suppose that for a finite type $k$-algebra $A$, we define two following properties:

- $A\otimes_k k'$ is a regular ring for all finitely generated field extensions $k\subset k'$.
- $A\otimes_k k'$ is a regular ring for all field extensions $k\subset k'$.

Are these two properties equivalent? In other words, is the failure to be geometrically regular witnessed by a finitely generated field extension?

Note that the second definition makes sense because the base change of a finite type algebra is finite type (so Noetherian, in particular). Definitions are those used in Stacks project, in the case it matters.