But L2 is just one point

That's an abstraction. In reality, what we call "L2" is an orbit around the L2 point. No shortage of room.

I was thinking since the point is so unstable, the orbit must be extremely small...

Boy was I wrong. The orbit is about the same size as the moon makes around the earth. [0] Its HUGE. We would run out of material to make satellites before we ever ran out of room.

[0] https://jwst.nasa.gov/content/about/orbit.html