The catch-up mechanism:
TWW professions each have a hidden currencies to track your weekly KPs, which is also a catch-up mechanism

3063 11.0 Professions - Tracker - Weekly Jewelcrafting Knowledge
3062 11.0 Professions - Tracker - Weekly Inscription Knowledge
3064 11.0 Professions - Tracker - Weekly Leatherworking Knowledge
3067 11.0 Professions - Tracker - Weekly Tailoring Knowledge
3058 11.0 Professions - Tracker - Weekly Blacksmithing Knowledge
3060 11.0 Professions - Tracker - Weekly Engineering Knowledge
3057 11.0 Professions - Tracker - Weekly Alchemy Knowledge
3059 11.0 Professions - Tracker - Weekly Enchanting Knowledge
3061 11.0 Professions - Tracker - Weekly Herbalism Knowledge
3065 11.0 Professions - Tracker - Weekly Mining Knowledge
3066 11.0 Professions - Tracker - Weekly Skinning Knowledge

Following is an example which I dumped in game during week 3.
/dump C_CurrencyInfo.GetCurrencyInfo(id)

currencyID=3061,
totalEarned=30,
quantity=30,
name="11.0 Professions - Tracker - Weekly Herbalism Knowledge",
maxWeeklyQuantity=0,
useTotalEarnedForMaxQty=true,
isAccountWide=false,
maxQuantity=36,
trackedQuantity=0

totalEarned and quantity is always same.
maxQuantity is the cap until that week.
These hidden currencies track KPs, except Algari Treatise and those unique KPs.

The currencies caps are dynamic added every week, just like crests.

+14 /week Jewelcrafting
+18 /week Inscription
+16 /week Leatherworking
+16 /week Tailoring
+16 /week Blacksmithing
+11 /week Engineering
+14 /week Alchemy
+14 /week Enchanting (changed from 15 to 14 since week 4)
+12 /week Herbalism
+11 /week Mining
+10 /week Skinning

(Blizzard realized when the growth cap was 15, Enchanting players always had one additional KP to catch up each week.)

If you want to manually calculate the caps instead of API, all region TWW 'Week 1' (not Early Access week) realm reset timestamps are FYI.

1725980400 -- us (2024-08-27 07:00:00 GMT-8)
1726027200 -- eu (2024-08-28 05:00:00 GMT+1)
1726095600 -- zh, kr, tw (2024-08-29 07:00:00 GMT+8)

Gathering professions and Enchanting:
It seems you have to complete all weekly KP items except Insc books, then the catch-up item begin to drop.

227662 Shimmering Dust -- Enchanting
224835 Deepgrove Roots -- Herbalism
224838 Null Sliver -- Mining
224782 Razor Talon -- Skinning

Crafting professions:
Patron Orders reward Flicker Knowledge (+1) or Glimmer Knowledge (+2)

228724 -- Flicker of Alchemy Knowledge
228725 -- Glimmer of Alchemy Knowledge
228726 -- Flicker of Blacksmithing Knowledge
228727 -- Glimmer of Blacksmithing Knowledge
228728 -- Flicker of Enchanting Knowledge (never seen)
228729 -- Glimmer of Enchanting Knowledge (never seen)
228730 -- Flicker of Engineering Knowledge
228731 -- Glimmer of Engineering Knowledge
228732 -- Flicker of Inscription Knowledge
228733 -- Glimmer of Inscription Knowledge
228734 -- Flicker of Jewelcrafting Knowledge
228735 -- Glimmer of Jewelcrafting Knowledge
228736 -- Flicker of Leatherworking Knowledge
228737 -- Glimmer of Leatherworking Knowledge
228738 -- Flicker of Tailoring Knowledge
228739 -- Glimmer of Tailoring Knowledge

Conclusion
I think it make sense.
catchupCount = maxQuantity - totalEarned - notDoneWeeklyCount(Not including Treatise)

As for Herbalism, Mining, Skinning and Enchanting, catchupCount should not be displayed before finishing other KPs of weekly sources except Algari Treatise.

(In fact, there are hidden currencies to track Algari Treatise, but they do not work for now, only the caps is added every week.
e.g. 11.0 Professions - Tracker - Insc Book - Alchemy Knowledge)

Regards

Was coming here to recommend the exact same thing but you explained it MUCH better than I would have. +1