Destiny 2 – Why Was My Drop Such a Low Level?

You described the differences pretty well.

In Destiny 1, shaders were normal items - they were not consumable. There was only one shader slot, and it applied to all your armor (weapons were not affected (related, most exotic weapons had one or two ornaments that worked similar to shaders, but were consumable)). You could change the shader at will, and the shader would not be destroyed. Later on in Destiny 1's development they added a shader kiosk where you could get a new copy of any shader you have ever found which would allow you to effectively use the same shader across all your characters.

In Destiny 2, shaders are now applied per item and can be applied to weapons, sparrows, ships, and ghosts in addition to armor. Shaders are also consumable - once you've applied a shader, you can't use it again. If you replace it with a different shader, the first shader is gone. When a shader drops, you typically get a few copies of it (I've gotten 3 at once, not sure if that is guaranteed).

The main issue some members of the community have with the new system is that in addition to being consumable (which means you tend to think about applying a shader, since you can't use it again), is that you can buy them with real money via the Eververse store. The conspiracy theory is that shaders were made consumable so that Bungie would make more money on microtransactions.

I am going to answer this from personal experience from leveling up 6 characters, it is possible there is something I'm overlooking or that theoretically there is a faster way if you maximize time.

The fastest way I've found is to first finish the story. Each story mission gives you a lot of experience. You don't even have to kill all enemies unless it specifically tells you to, you can avoid them and just get to the end. But this will mean you might have to do some adventures or public events to level up enough to access the next story mission.

Once you beat the story and get to level 20 your next mission is to get to raising your power level. "Powerful gear" AKA Luminous engrams are your main goal, these will give you legendary (and sometimes exotic) gear at a power level higher than your current max. You can get a number of them each week by completing milestones. An easy one to get is by joining an active clan and once members of the clan complete weekly milestones (even without you being there or online) they will unlock and give you the rewards. There's also exotic quests which lead you to guaranteed higher level gear and unique exotics that you can only get through the quests.

After climbing high enough you'll be able to play end game activities such as Nightfalls or Raids. Completing these weekly will not only give you more luminous engrams but these kinds of actives also have a higher chance at giving you exotics. Rise and repeat each week getting as many luminous engrams as possible and with enough time (and luck) you'll be at max power level soon.