In this scenario there are two spacefaring empires, each with a handful of solar systems under their control. The two empires have been adversaries for millennia.
In each solar system there are habitable worlds. Any indigenous population on these worlds was forcibly conscripted into the empire that found them first and operate as a vassal state. Unoccupied worlds were populated.
The technology in this scenario allows for planet-to-planet travel in a matter of hours. Imagine 1 hour from Earth to Mars, or 10 hours from Earth to Uranus for scale, something akin to air travel for us now.
System to system travel, while faster than light, still takes centuries. Neighboring systems might be 200 years, while the frontier systems may take 800 years or more to reach from the core worlds. Most of the beings in this universe have a life span similar to humans - assuming technological advancement in health care and gene-therapy, maybe 200 years. Cryogenic suspension is possible but difficult.
The question is: What does this war look like?
Sending a fleet to assault a system would take hundreds of years and several generations, and would be seen coming decades before they arrive. Also, those ships would be unavailable to counter some other offensive launched against their civilization.
I have a few options on the table already:
Attaching drives to meteors or other large space rocks and launching towards the expected location of the system. These could travel faster than the ships, maybe decades instead of centuries. I assume these species could to the math for where to aim them.
Ships full of robots, again these could go faster than 'squishy' ships. They would be hard pressed to accommodate changing commands though.
Ships with no crew but full of bio-weapons.
Note: For the sake of the story, let's assume communication is near-instant across systems.
Just to provide some clarification, each side of this war has a deep-seated, almost religious belief that their empire must be the one to control the stars. There's nothing political about the war, it simply must happen, and must continue until one side wins.
Second, neither side wants to rule over a galaxy of glass balls in space. They know that habitable planets and populations are valuable. Each side wants to conquer the systems while still having something to rule. Since all but the original system for each empire was forcibly conquered in the first place, a change of allegiance is realistic. (Perhaps several systems have been passed back and forth already)
They would be willing to 'nuke' a planet or two if necessary, but for the most part the goal is to take control of the planets under the other empire's control.
The 'vassal state' planets are effectively doing their own thing in terms of society, but they are directed by the overlords to help the war effort - for example 'attack planet x' or 'build shipyards'.
First of all, thanks everyone for the feedback and ideas. It's a lot to wade through and there a lot of ways this could impact the universe I'm thinking of, I'm going to need to unpack it all in my brain.
Second, I need to apologize because I muddied the question by referencing FTL. My intention was to ask what a war would look like without planet to planet travel times being short, like in Star Trek or Star Wars. Going back to my old math / notes, the speed I'm looking at for ships is about 10% of Light speed, or around 1,000,000km/h.
At this speed, Earth to Mars would be less than an hour, Earth to Uranus about 25 hours, and Earth to Alpha Centauri would be 42 years, Earth to Wolf1061 would be 140 years, etc... Not accounting for acceleration issues, if there are any with this level of technology. I want it to be somewhat science-based but a little handwavium is OK to keep the story entertaining (it will use real star systems and their real distances for example, but somehow maybe the aliens all have a universal translator).
Third I think technology of the two main factions would basically have plateaued. The vassal planets might not all have an even level of technology, but overall there aren't any game changing discoveries that change the balance of power on a regular basis any more.