You say the state already has the dollars, but it will need more as BTC flows into the country.
Does the state handle the conversion - ie I sell my BTC to the state and it imports the dollars? This is the part I don’t understand is what part brings in new dollars at a lower cost than Western Union.
How El Salvador keeps it's physical cash in flow with a foreign mint is an interesting question but it is somewhat decoupled. Unless people are hoarding US dollars, the banks are getting them back as later deposits so the amount of physical dollars has very little to do with incoming and outgoing digital payments.
By the way, when El Salvador imports products from USA it most likely doesn't pay with cash so the net transfer of physical currency might be very close to zero.
How do they do electronic payments? Regular bank wire transfers. The fees are merely unattractive for small amounts. Western Union is a service for the unbanked.
Does the state handle the conversion - ie I sell my BTC to the state and it imports the dollars? This is the part I don’t understand is what part brings in new dollars at a lower cost than Western Union.