There are no serious implications for astronautics the science.
There are serious implications for the space tourism market, namely they're hard-to-fake signals that it's safe enough for passengers. We should all favor that market if we hope to one day stop subsidizing space travel but still have space travel. It's not without downsides though, and many ...
They both entered such trajectories that when the craft was not propelled by rockets but was freely moving under inertia the people inside it experienced weightlessness. That is achieved in the "vomit comet" only when the craft is guided through the air along just the right path rather than allowed to move freely by itself.
Is this all just advertising, or do these events carry serious implications for astronautics? Am I simply mistaken (very likely - I'm a complete layman) or have large parts of the media fallen for (or bought into) a publicity stunt?
The reason these are important is that these are privately developed and funded vehicles. Yes, SpaceX is privately owned, but ...
Did they reach space?
The Virgin Galactic SpaceShipTwo class craft "VS Unity" flew Branson up to 53.5 miles (86 kilometres). This altitude is considered "space" by the US air force, and nobody else. It is above most of the atmosphere, and does provide a nice view of the Earth.
The Blue Origin New Shepard class ...