The current data supports a value just less than 14 billion years. That
age is sufficient to encompass observations made so far.

Is those 14 billion years calculated with regard to the effects of
gravity and curved spacetime upon the lightspeed?

You do know that even the light is subjected to the effects of
gravity? Einstein even said so himself.

You don't need any mass to be subjected, if the spacetime continuum
itself is curved.