To add to this, this "square root" operation done to derive the Dirac equation is where spinors i.e. electron spin i.e. the Pauli exclusion principle i.e. the reason atoms exist at all comes from. Likewise antimatter. The "second order in time" of the Klein-Gordon equation comes from adding relativity and the "fix" reducing that to first order time is the source of antimatter and spin.

So yes very much so relativistic effects are a foundational part of QM.