I read this sentence,
"Home of the stars and gateway to the heavens, the Astral Plane teems with excitement and possibility,"
to mean:
The 5e astral plane is itself the home of all of the stars in the universe of the material plane.
This is why it is called the "astral" plane.
Even so, the actual stars are in the aspect of the astral plane, called "wildspace". It is a way to handwaive the reallife distances between stars.
Meanwhile, the astral sea the astral plane proper, the one that the Players Handbook describes. But this astral sea is a realm of though and dream and lacks spacial distances.
Thus:
• "home of the stars" describes the wildspace.
• "gateway to the heavens" describes the astral sea bordering the celestial planes.