Your crucible/vanguard tokens will stay on your character and you can turn them in next season.
Saving powrful rewards won’t reward any gear over 650 in the new season. You have to earn new rewards in that season to see the power level increase.
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They way gear drops is that it’s based on your current max possible level, and not the level of what you have in that slot, when the engram drops. So for example if you’re at 300 and then grind to 600 without turning in the engram it’s still going to be a 305 level piece of gear. The only time you should put of turning things in for higher light is quest rewards. Those you can put off picking up while you raise your light and actually watch the level on them going up.