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I understand that any wave can be given direction using a setup like a phased array.
As I read about the properties of EM waves, I find that microwaves are unidirectional in nature.
What is it about its nature that gives it this directionality? Is there something similar for giving radio waves omnidirectionality?
No, microwaves and radio waves are both electromagnetic waves. The difference is the wavelength, microwaves are much shorter.
A directional antenna should be at least some to many wavelength in size. So a directional antenna for microwaves may be about a meter to several ten meters in size if the wavelength is about some millimeters to several ten millimeters.
If radio waves are several ten meters long, a directional antenna becomes very large.
Visible light is an electromagnetic wave too and there is unidirectional as well as omnidirectional light.
The Sun radiates light in all directions but after the huge distance from Sun to Earth the light is pretty much unidirectional. But star in a distance of several light years is a much better unidirectional emitter than our Sun if both are viewed from Earth.
microwaves are radio waves.
We typically define "microwave" to be any electromagnetic radiation (we'll come back to that word in a minute) between ca. 300 MHz and 300 GHz. So, your remote garage door opener, your mobile phone, your Wifi, your automotive radar, your satellite dish: all microwave devices.
Radio wave is any electromagnetic radiation that's not high-frequent enough to be considered light (or even X-rays). So, radio is a strict superset of microwave, any microwave is a radio wave, by the definition of these words.
For radio waves that fall into the microwave region, the exact same physical rules as for waves that do not fall into the region apply. Exact, because they are literally the same phenomenon – Maxwell's equations leading to a periodic exchange of energy between magnetic and electric field, which leads to propagation at the speed of light. Light, by the way, is also just another wavelength region of electromagnetic radiation, and the same physics apply.
I understand that any wave can be given direction using a setup like a phased array.
Correct, but to be able to build such an array, you need to achieve coherent phase at all the elements of the array. This is technologically very doable for most of the radio frequency range, so, from basically > 0 Hz to 300 GHz, but for that array to actually do much, it must also have dimensions in the order of magnitude of the wave's wavelength. And for example, for ELF (extremely low frequency) submarine boat communications, the wavelengths is > 10,000 km. You need a gigantic spaces to build just one antenna, so, practically, an array of such is pretty much impossible (also, makes little sense, there are no submarines many wavelengths from the transmitter – that would be deep in space).
On the other end, it's hard to make light that has coherent phase and keep that over distances. A laser is a single source of a coherent electromagnetic wavefronts, and that's why you'd want to use it in communications, and if you need anything with a very nicely defined beam. So, while not a phased array, the optical lenses in front of your laser are really analogous to the dielectric lenses in front of satellite uplink dishes, for example, as they shape the wavefront by combining them with different phases – just like a phased array does, just scaled down by the factor between your microwave wavelength and light wavelength.
