@TheBlizWiz Of currently somewhat active shops according to forum posts:
No shops currently have two-way exchanges. (IE if I have 64x I can get 1y out of the shopkeeper, where the price is 1y for 64x.)

Gold:
Haxington Oreburgh Mine: 8 ingots = 1 diamond
Andureil: ~14 ingots = 1 diamond
Ealdwine: 64 ingots = 1 diamond

Iron:
Haxington: 16 ingots = 1 diamond
Ealdwine: 64 iron = 1 diamond

Diamond:
Everyone: 1 diamond = 1 diamond
Everyone: 9 diamonds = 1 diamond block

Emeralds:
Ryebye: 1 Iron Horse Armor = 3 Emeralds
Ryebye: 1 Gold Horse Armor = 2 Emeralds
Andureil: Knockback 2 Book = 5 Emeralds

Cobblestone:
Haxington: 256 (4 stacks) = 1 diamond
Ryebye: 320 (5 stacks) = 1 diamond
Ealdwine: 384 (6 stacks) = 1 diamond

The first numbers listed are shops that have not recently been updated for a while. The last numbers are the shops that have been recently updated.

The value of different items are decided by its demand and supply of the market and individuals?

I agree with the point that the diamond is too high a value to use as the basic currency unit, and indirectly inflates the value of everything else.

I think it just takes one merchant with the resources and time to establish a baseline price of diamonds to emeralds. Then the value of emeralds would become tangible. In the past the npc Spawn merchants did this, now the active player-sellers would need to step up if this is what all the players want.

Merchants with an assortment of book vendors and a strong business are in a great position to take this on as the emeralds seem to mostly get consumed buying book enchantments.