> Starship will deliver millions of tons to orbit and beyond per year

Excuse my naive physics, but is there a point at which if you take enough mass off of earth and launch it into space, it would have a measurable effect on earth's orbit? (Or if the mass is still tethered to earth via gravity, is there no net effect?)

Earth weighs about 5972200000000000000000000 kg. They are claiming to plan to launch ~5000000000 kg / year. That's 8x10^-14 %. You'd need some pretty accurate instruments to tell the difference.