Kings being the sovereign will almost certainly create the coinage as you would expect. I imagine the gameplay wouldn't be heightened much by every kingdom's coins being of different value so more than likely they will all equal the same amount. Things like inflation and general wealth of the differing kingdoms could cause one kingdom's money to technically be worth less though much like some currencies are worth less than the dollar in our world.

The contract system should allow for creation of promissory notes can can be traded or given to third parties for enforcement. That is all that is needed for private bank notes, and private bank notes work as currency (and historically were lighter and easier to carry). These usually have a stated value in reference to some other currency, but could also be linked to any stuff (eg 50 crates of mangos).

Even historic currency acted that way (gold standard notes).

If you are asking if a person can create some private fiat or cryptocurrency not supported by any promised exchange of something of real value, we don’t know and I don’t see why anyone would want to use such things.

Historically, money was worth the value of precious metal that was actually in the coin. If you were in Country B, you went to a moneychanger/banker to exchange your Country A gold pieces for a Country B gold pieces. Or exchanged those same gold pieces for local silver pieces. The moneychangers/ bankers know how much the coins from each realm weigh and what %age precious metal they are (how "debased" they are). They make the conversions then hand you the right amount of coinage. That means transporting large sums of cash was both dangerous and very heavy. That's how banking (and promissory notes/ script) started...

what we know of currency right now is each kingdom will have their own coinage at launch, then people can mint those coins. they have also stated that dukes will be also abe to make/mint their own official coinage. now this is all tbt/wip so who knows the actual system