If the Apothecary job and its daily is supposed to be very late game and high difficulty, please ignore this! Barring that...

Apothecary seems disproportionately hard to both unlock and use due to the rarity of Chamomile. I have had 10+ cats on gathering and herbalism for over a week - plus a lot of gathering for several beforehand to do things like craft a library - and gained maybe 5 chamomile. Give you need 3 every time you want to product tea leaves - this is a very, very slow process.

Compare it to every other job.
Builder, Mason, Craftscat, Herbalist, Gardener, Flockherd, Clothier - All (optionally) take common resources, or resources that can be common (i.e. clay from mining)
Scribe, Artist - uncommon (items are 4-6 notes in MP)

Apothecary is the only one that requires a rare item - and it's so rare that the MP price rarely drops below double the WW price. There's even sometime none for sale in the MP. Increasing the drop chance somewhat would make it more viable (particularly when Adventuring turns up and people want those items as well) and bring it more in line with other jobs.

(I genuinely wonder if there's a typo in the drop chance. Catmint is supposedly the same rarity, but despite only using jobs that drop both (gathering and herbalism) I gained over 3x as much catmint in the same time. RNG is RNG, I know, but it's a massive discrepancy over several weeks)

EDIT: Just noticed that Wintermint is an Uncommon from Herbalism. Now convinced that it's an error in Chamomile's drop chance, as it does not seem reasonable to make a job much harder at some times of year than others.

Can't say whether the drop rates are intentional or not...

But depending on how much tea you plan on making you might not need to do the apothecary daily every day

I haven't had a cat assigned to apothecary in A While since most of the crafts requiring tea leaves are adventuring gear which i have no need for at the moment. My chamomille has just sorta slowly been building up in my inventory.
I do think that if i were to permanently assign a cat to apothecary that I would run out of chamomille at some point, but then I'd also end up with an absurd amount of tea leaves

There are in fact multiple of the daily jobs that i only do occationally or where i have one cat taking care of three jobs (I just don't need That Much paint )

Apothecary was designed to be late game yes, but it might be worth asking about if it's giving you this much grief

Same as fae above, I don't have a dedicated apothecary cat and I let my chamomille stocks build up for a while, then set a cat or two on apothecary when I need tea leaves, then switch them back when I run out. My tea making was only stopped by lacking flowers and never tea leaves, so personally I can't say I've felt that chamomille was dropping too little (especially considering that I've been brewing adventuring related items as well on the side.)

... I have 73 Chamomile and 29 tea leaves and I've made abut 3 catmint teas in my time. My dedicated Apothecary is currently in someone else's village

Apothecary is indeed a lategame unlock and theoretically is going to be the last job you get. Definitely worth looking into the drop rates to see if they're intentional, but if they are, I'm fine with how things are. I imagine Chamomile will be a potential Adventuring drop even if it is rare, but that'd at least make it a little more easier to get. Right now things are a bit rough because Gathering is fixed in the number of times you can actually do it per day.