How does Destiny 2 save?

Gear will be saved the moment you acquire it.

Mission progress will be lost if you quit. Most of the time, missions are short enough that it should be considered "acceptable" if you have to quit early. Once a mission is complete and you return to the solar system map, that mission counts as completed.

The intro tutorial is actually a collection of missions, and I'm pretty sure if you quit during one, it will bring you back to the most appropriate starting point.

There are checkpoints in some missions that it reverts to if you die, but these aren't stored after quitting.

Destiny and Destiny 2 are always online RPGs and the games will be continuously saved. It would be almost impossible for progress to be lost, and there is no need (and no possible way) to manually save.

Go ahead and play and quit whenever you like and you won't lose experience, gear, or bounty progress. But if you are in the middle of a story mission, patrol mission, strike, raid, crucible/gambit match, ect then that progress will be lost and will need to be redone.