So how do we collect these project stuff?

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Sorry, it's a little long and I'm lazy lol. Can you get the augmented caches without rp? That's my only question.

You can only get one augment cache without spending RP by using the cache fragments you get in the ashe/ekko/kat and disruption caches. Hypothetically you can get 2 if you're lucky and your one cache happens to have another fragment inside of it.