EIRP is a measure of the maximum power in any direction, so a phased array that transmits 1W only forward has the same EIRP as an omnidirectional antenna that transmits 1W forward, but also 1W backward, and up, and down, etc. Overall the omnidirectional antenna may transmit much more power total, but still only 1W in any particular direction.
By definition, any antenna with positive gain must concentrate power in one or more directions. So in practice, omnidirectional antennas are only omnidirectional in the horizontal plain, they have greatly reduced power in the up and down directions (which makes sense as generally there is no need to transmit into the sky or ground).
> Overall the omnidirectional antenna may transmit much more power total
This doesnt make sense - an antenna is a passive device, not an amplifier. Regardless of gain, you cant get more energy out of an antenna than you put into it.
So if you're transmitting 1 W and your antenna has a gain of 30 dBi (1000x), that's equivalent (from the perspective of whatever it's pointed at) to an isotropic antenna (no gain) emitting 1000 W at the same distance.
It should be obvious that EIRP is what matters for interference and human safety, hence why the FCC regulates EIRP instead of power output.
A phased array is a very high-tech method of selective transmission so that you can send a radio signal that is stronger in one specific direction. The way I think of it is that it creates a virtual directional antenna where the direction is adjustable without actually physically moving the antenna elements. The actual tech involved is pretty heavy math and physics (and I don't fully understand it myself) so if you want to really understand it then you may still need to spend hours reading about it.