Theory can say what shape the universe should have, for example inflation predicts a flat universe[2]. Of course you then have to check if the theory matches what we observe.
As far as I've gathered, the current measurements are consistent with a flat universe. Here's[1] a post about a recent, improved measurement.
As far as I've gathered, the current measurements are consistent with a flat universe. Here's[1] a post about a recent, improved measurement.
[1]: https://astrobites.org/2020/12/03/cosmic-clocks/
[2]: https://en.wikipedia.org/wiki/Flatness_problem#Inflation