My son with workshops your better off selling the produce manual instead the best is the armour workshop. i hope this wisdom will benefit you in some way

The economy can get pretty messed up, you need buyers in order to sell. Caravans can help, but you'll find things like sake will pile up and never make a profit. Industries too close together can ruin the market. It got me to try caravans and they are actually pretty good in this mod. Though all my fiefs now pay me thousands in profit a day anyway. If you really wanna use workshops, the advice from the first reply is good. You can put inputs into the warehouse and have them put outputs in as they use them. This is managed in the clans/other screen

I am seeing this all too and a Part of it i feel is that the Ai changes up their workshops too often. Im mainly hanging out in the Saikai lands on Kyushu and I have noticed that all the workshops have gone from being fairly balanced / diverse to just... bad? lol im not sure how else to describe it but it then seems to have thrown off the economy of the entire island!
A specific city example - Tachibanayama seemed like a great industrial city that had a Weaponsmith, Armorsmith, and 2 other different things. But after a few trading trips around the island I come back and see that it has 3 Sake Distilleries and like a Weavery.... no way any of those Distilleries are making money
After seeing that I paid more attention as I was going around and Noticed that after something like 10-15 days a workshop will have changed in a city (or it feels like it), No production seems to every really be stable
This plays havoc with my Workshops as one week they will be making good sales on say Sake but then the next week sales tank because all the surrounding cities suddenly opened several of their own Distilleries, even without good Imput

There is also an issue of cities going bankrupt, which makes your once profitable workshop income go 0.

This is also tied to consumption of the ressources.
Cities with many tradebound villages (like Edo) get many villagers and caravans who "consume" the crafted items, while providing the city with raw ressources.

But cities with low traffic cant really sell the produced products fast enough, so over time your profits will get less and less.

Its abit of a deathspiral:
- Workshop sells to the city
- city goes bankrupt
- City cant buy raw ressources
- raw inputs get more expensive, produced products get cheaper until its not profitable anymore,
- city slowly manages to get more gold
- until the death spiral begins again

It also seems like the base production of certain ressources is just too much, like rice, sake, fish, etc., the cities are covered in hundred thousands of food, which makes food kinda pointless, as it can never be scarce.