The bottle is the artifact
When you finish a potion, vanilla hands you a brand new, anonymous glass bottle. The mod copies your enchantments onto it instead. That single decision is what the whole mod is built on: the enchantment is a property of your bottle, not of the drink, so the real cost of an enchanted potion afterwards is just the brewing.
Tip: Pouring a potion into a cauldron gives your enchanted bottle back too, not only drinking it.
The stack sets the level the table asks for
This is Flavor Text's ladder, shared: 1–16 bottles asks for 1–8 levels, up to 48–64 asking for 24–30, and bookshelves scale that from 15% at none to 100% at fifteen. A full stack of 64 reads 1 / 3 / 5 at a bare table and 10 / 20 / 30 in a full library. There is no randomness in the number.
Tip: You still only pay 1, 2 or 3 lapis and levels for the three rows. The big number is a requirement, not a bill.
One potion is a full commitment
You can also bring a potion you already brewed and improve that. Potions do not stack, so the ladder asks what share of a full stack is in the slot rather than a raw count, and one potion out of a possible one is everything you could have committed, which means the full level-30 ladder for a single bottle of Strength. Empty bottles are the efficient route, sixty-four at a time; a filled potion is the reactive one you take when you want this potion better right now.
The enchantment survives filling and brewing
Every hand-fill in the game goes through one shared piece of vanilla code (water source, dragon's breath, cauldron fill and cauldron empty), so a single hook carries the enchantment in both directions. Brewing is bracketed too: the brewing stand builds fresh potion stacks that would otherwise throw the enchantment away at the first nether wart, so the mod snapshots before and restores after. The one exception is honey: beehives build their honey bottle by hand instead of going through that path, so honey is out of scope.
Two kinds of enchantment
Half of them read the act of drinking and work on anything, including plain water: Chug, Refreshment, Cleansing, Fortifying, Springwater and Last Drop. The other half read what is in the bottle and need an actual brew, namely Prolonged, Potent and Round of Drinks. Two treasures, Everflowing and Vintage, are never offered at the table at all.
Tip: Springwater and Refreshment make a water bottle a real early-game item. The author flags that as one to watch.
Vintage: potions age in the bottle
A Vintage bottle's contents gain +25% duration per in-game day, capped at +100% after four days, which is about eighty real minutes. The tooltip reads out 'Aged N day(s)' and the bonus, because a treasure whose whole mechanic is invisible waiting would otherwise read as broken. The clock restarts every time what is in the bottle changes, so an awkward potion that aged four days does not become a pre-aged Strength potion; each brewing step is a new potion.
Tip: Vintage and Everflowing are in different exclusive groups, so one bottle can carry both, via the anvil.
Everflowing's cooldown locks every potion you own
The drink is never consumed, with a thirty-second cooldown between sips. Minecraft keys item cooldowns on the item type and every potion in the game is the same item, so that cooldown locks out your emergency healing potion too. This is kept deliberately: the infinite bottle is your sustain, not your combat rotation, and it renders as the ordinary cooldown sweep for free.
A full enchanted bottle is a dead end, on purpose
Once a bottle is both enchanted and full, nothing will add a second enchantment to it. The table refuses because vanilla insists an enchantable item's enchantments be empty, and the anvil only accepts empty bottles. The way through is to empty it: drink it or pour it out, get your enchanted bottle back, and put that on the anvil. The loop is enchant, fill, drink, anvil, fill again, and the only thing you can never do is upgrade a potion without spending it.
Tip: Keeping the anvil to empties makes the two treasures a decision you take before you brew.