Never underestimate the bandwidth of a station wagon full of floppies, or in this case a boat full of books.
Communication over this empire would vary based on urgency. A tall tower on a world of that size could be seen as far as atmospheric conditions allow and the brightness of the signal flame permits.
So start with a set of towers. These towers have lights on them. They'll have to be fire based: mirror based will be washed out by ambient light (assuming this planet has a night and day cycle somehow), possibly with lenses and shutters. A signal would be sent to the nearest cities, and relayed along.
Extra tall/bright towers could skip over more than one city in some cases.
The level of haze will matter. On hazy days, signals are going to fail. On extremely clear days, you might be able to do something fancy like send different messages in different light frequencies (where the other side has filters to extract the the two channels).
These messages require an economic system that crosses from one city to another and clears payments. They are also going to be reasonably expensive.
Other messages will be sent by messenger bird or boat. Sometimes complex messages will be sent by boat and "saved" to be referenced by light or bird-based messages (contingency plans and the like).
Security of these messages can be maintained by use of one-time pads. So the crown could send messages security to a general through multiple paths and not worry about it being intercepted, because the general has a key (transported physically) that ensures the message package is noise without it.
Having modern information technology could be useful. Routing of messages (around damages caused by clouds, rain or hostile forces), compression, and other techniques would all make their communication network better.
Mountain ranges and other similar stuff could cause problems. With the elves living near the coast, overland messages are difficult. Either building towers on the mountains, or hiring non-elves to do so, would permit short cuts. Use of slow-delivery one-time pads or other encryption could prevent the towers from corrupting or intercepting messages.
The bandwidth you'll get from boats will far exceed the bandwidth from the light towers, so passing huge pairwise common one-time pads around shouldn't be all that expensive compared to maintaining and using the towers.
The transparency of air increases the farther you are away from the ground generally. So making balloons that float above the cities that relay messages to other cities might even be practical, and would match the steampunk sensibilities of clockwork submarines. You could even imagine large ground-based lights shining up at the balloons, who have huge mirrors and shutters to beam the message to the target. Spotter balloons in the destination city with large telescopes would then record the message, and use mirrors to send it down to the city below.
Said balloons could also send messages to predetermined locations for fleets. A fleet might have a few balloons and some extremely bright flares it can use to communicate limited information back to the nearest city state.
Using data for death rays, light in completely clear air at sea level loses about half its intensity every 30 km. In more realistic situations it is more like every 1.5 km. So height (and lower air density) is very important.
At a 6 km altitude air is half as dense. And it might be far dryer and have less particulate in it. However WW2 barriage balloons (tethered) only managed 1.5 km. Still, 1.5 km might result in far less moisture, particles, and a decent reduction in air density (20% ish) and ability to see over smaller mountains. (6 km is too high for tethered, and unless you want airship elves isn't practical).