Destiny 2 – Is it Necessary to Complete Every Character’s Story?

The two ways as far as I can tell: (After maxing my warlock subclasses)

1) Leveling up, you'll continue to earn them this way past 20 until you've filled out all the skills in a class.

2) Doing adventures that have upgrade points as a reward. If you've fully upgrading each subclass these rewards will change, usually into blue engrams in my experience.

3) If you do meditations and still need upgrade points you can get them from those.

From the wiki

Nonetheless it was captured at the start of Destiny 2 by the Cabal Red Legion and taken from humanity, weakening Guardians severely, only to reawaken after countless millennia to smite its leader Dominus Ghaul and putting an end to the Red War.

Basically, Ghaul caused the Traveler to wake up after being put under the amount of stress that "draining the Light" caused. Ghaul mistook this for "seeing him", but it's more than likely still unaware of individuals the same way a human is unaware of individual ants.

At this point however, nothing more is known about the Traveler, other than it is now "awake", as it does nothing else after this point*.

^{* I have not played the DLC, so I don't know if this uncovers anything more about the Traveler}