Space is huge, but most of it's boring. Rather than tracking where people are or have been, track where they're going.
Each system would be responsible for its own detection (and probably interdiction). String up sensors near your planets and other important bodies. They can be anything; visible light is fine. If they detect a ship, you hail it and demand and (automatic or manual) response code of some kind. If you don't get it, you impound the vessel.
Some false positives from e.g. asteroids are inevitable but easy to clear. False positives from friendly ships that are just misinformed about your codes give your bureaucrats practice in yelling at bureaucrats from other systems. Anything you net from the other empire is the diplomats' problem.
Ships would have virtually unfettered access to interstellar space, meaning you'd need another means to detect things like muster or rendezvous points in deep space. However, in order to do anything meaningful, at least one ship has to come near one of your planets (moons, stations, asteroids, whatever) eventually. Aside from an invasion fleet, you should be able to intercept any clandestine activity as it approaches its destination.
This setup does require each of your systems, even ones not near the border, to be warded, but you're going to want to do that for law enforcement and traffic control reasons anyway. (It will protect you against things like smugglers, as well as the potential hazard of ships moving through your systems any old how, without necessarily knowing what other ships or hazards are around.)