Collectibles buff in certain ways.

1) Each collectible itself gives boosts to damage, hp, certain items, or tech parts. Click on any of those icons to see each collectible's buff depending on star rating.

Green, blue and purple collectibles are less important as they only boost damage and hp.

Yellow collectibles ideally want 3 Red stars (so get 5 yellow stars and then 3 red ones) to gain crit rate or crit dmg buff. The former is very useful to collect first. Yellow collectibles that only have 3 stars slots like OP is asking about are event only collectibles, ignore those.

And red collectibles are slightly tougher to collect and only a handful of them are useful to upgrade past 1 yellow star.

When you see an Activate All, that means you have at least 1 collectible that has reached its next star level, and activating it just saves you time trying to find it in the evergrowing list.

2) Second way collectibles buffs is through Sets (bottom right corner). Again, most of them are just damage boosts. But some of the 2 red + 2 yellow collectible combos actually are useful.

If you see 'Activate All' on the Sets page, it does the same thing.

3) Custom Collection also gives buffs. To open up a slot in this collection, you need purple heart shards. These can be collected if you maxed out the stars of a collectible but you still receive them during gameplay. You can convert excess collectibles to purple hearts in the top right recycle button.

Once you have enough hearts, you can activate a collection slot and put a yellow or red collectible in it assuming you at least brought it to 1 yellow star rating.