Radars aren't omnidirectional either, but there are several types that might be detectable.

The old Ballistic Missile Early Warning System (BMEWS) radar sites at Clear, Alaska, Thule, Greenland and Flylingdales in the UK each used to have fixed detection fence radars along with 3 powerful tracking radars. The fixed fences projected a consistent energy pattern over the North Polar region and waited for a missile or space launch to penetrate. When that happened, one or more of the tracking radars would swing over and begin a high precision track. Those were very powerful radars and they operated for decades. Today, somewhat lower powered phased array radars are used at the BMEWS sites to perform the same functions. Phased arrays like the Cobra Dane radiate with a peak power of many megawatts and depending on the radar's mode (missile warning, intel, or space surveillance), all of that energy can be concentrated into wide areas or very narrow beams.

Radars typically project either fences or beams. The beams, like lasers, don't follow the inverse square law because that law applies to omnidirectional broadcasts. They have very precise pulse repetition characteristics like a pulsar, but they can also change modes which would indicate the pulses are artificial. Radars have been in operation for over 60 years. Of all the RF emissions on Earth, they might be the best indicator that life exists on Earth.

High powered lasers could be built to operate as a beacon (whether that's a good idea is a different matter), but their narrow beamwidth would mean we'd need to concentrate on the best candidate star systems. There are other operational questions, such as how long would we aim at a particular star system before moving to the next one? After all, had someone tried to use such a technique at the Earth 100 years or so ago, we might never have noticed. Likewise, if the laser signal had arrived during daylight at most telescopes (or had the telescopes been looking in a different direction), it probably wouldn't have been detected.