I have done some work on testing retainer stats requirement for extra yield. Here are my results:
Gathering Retainers (MIN or BTN)
(Gathering/Perception)
3010/2935 = lvl 83 30 pieces, but lvl 84 20 pieces
3018/3016 = lvl 84 30 pieces, but lvl 85 20 pieces
3018/3076 = lvl 85 30 pieces, but lvl 86 20 pieces
2995/3175 = lvl 86 30 pieces, but lvl 87 20 pieces
2995/3195 = lvl 86 30 pieces, but lvl 87 20 pieces
2995/3201 = lvl 86 30 pieces, but lvl 87 20 pieces
2995/3215 = lvl 87 30 pieces, but lvl 88 20 pieces
2995/3261 = lvl 87 30 pieces, but lvl 88 20 pieces
2935/3306 = lvl 88 30 pieces, but lvl 89 20 pieces
2935/3377 = lvl 89 30 pieces, but lvl 90 20 pieces
2935/3411 = lvl 89 30 pieces, but lvl 90 20 pieces
2935/3417 = lvl 89 30 pieces, but lvl 90 20 pieces
2935/3419 = lvl 89 30 pieces, but lvl 90 20 pieces
2935/3420 = lvl 90 30 pieces!!!
2935/3435 = lvl 90 30 pieces!!!
So the MAGIC NUMBER is 3420 Perception!!!
Gathering has no impact to that extra yield once you got pass the Gathering requirement stated on the item list when you do your ventures. So ZERO melds of gathering on your lvl 90 gear!
In terms of the melds required to achieve 3420 Perception, you don't need any Grade 9 / 10 materia at all. I used PURELY Grade 8 or lower to achieve that amount. Some light overmelds were needed. But most gear just need 1 overmeld (with the exception of the hat and offhand).
Below are my melds on my retainer:
MH & OH required 1 overmeld using Grade 8. OH needed a 2nd overmeld using Grade 7.
Hat is not maxed. One could have added even more perception there if need.
Chest, gloves and pants are all maxed on Perception with the above melds.
Shoes could have added 1 more perception. But actually, we don't need that much here... I could have used a Grade 5 instead of a Grade 6 for that overmeld. There will be 5 perception less, but you can see from below that I have 3425 from these melds. So -5 is still fine.
I used Grade 7 for all my overmelds here, but one could have used Grade 6, which is even stronger. I just didn't have enough Grade 6 for overmelds. If you have a lot of Grade 6, you could use that instead, and that will give you a boost of 2 more perception per accessory. That extra 10 perception you gain using Grade 6 would allow you to subtract 10 perception from somewhere else.
Here's my final retainer stats from the melds above. Note that I could reduce 5 perception from somewhere, and it would have been fine.
This is just to show that I could have used this meld instead to reduce 5 perception.
This is just to show that I could have used Grade 6 instead on all my accessories' overmelds, and I would have 2 more perception per accessory.
Finally, if you run out of Grade 7 / 8 materia, you can always get more from Qitari Beast Tribe vendor using those tokens. It's a good way to utilize those old tokens!
As for Battle Retainers, I do not know that much. All I know is ilvl 555 will give 12 pieces of lvl 86 mats, 10 pieces of lvl 88 mats and 7 pieces of lvl 89 mat. Good luck testing these!
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EDIT on 2023-01-26:
Patch 6.3 Retainer Stats Threshold Test Results on Post #19:
https://forum.square-enix.com/ffxiv/...=1#post6173552
Copied post below:
It's Patch 6.31 now. Today, I have experimentally tested and confirmed the following retainer stats in the game:
Honestly, unless you regularly use a lot of Alien Onions, it's NOT worthwhile to go as high as 4107 perception (probably just need 4104 as Silverbane has suggested above from prediction) on your retainers. It takes almost a full set of i620 Indagator's gear with very strong overmelds. It burned out a lot of my materia stashes just to confirm this.
4020 perception is worthwhile if you wanna gather 50 pieces of Chondrite/Integral Log per run. It takes at least 2 pieces of i620 Indagator's gear as well as both Indagator's mainhand and offhand tools with Grade 10 materia overmelds to achieve this much perception.
Meanwhile, 3687 perception is very achievable with a mixed combination of i560s, i590 Pactmaker's and i620 Indagator's gear, with reasonable melds.
Personally, I have 1 retainer currently >4020, and all other retainers >3687.