May seem really daft but I don't know of any ways of detecting redshift in the rest of the EM spectrum, so was just wondering
Redshift is said to have happened when the wavelength of electromagnetic radiation increases. Blueshift, a sister phenomenon of redshift, is said to have happened when the wavelength of electromagnetic radiation decreases.
In the visible light spectrum, the red color has a longer wavelength, around $700nm$, compared to other colors; Violet, for example, has a wavelength of $400nm$. When the blue light gets redshifted, i.e: its wavelength increases, it becomes redder. Hence, the name redshift. Though the word 'red' exists in the name, it has got nothing to do with red or visible light. This redshift phenomenon affects radiation of all wavelengths: gamma rays, x-rays, ultraviolet, visible light, infrared, microwave, radio waves and everything else in the electromagnetic wave spectrum.
Bonus: Redshift and the expansion of the universe (the big bang)
The redshift in different wavelengths of light measured from different galaxies is an indication that the galaxies are moving away from us. These observations not only indicate that galaxies are moving away from us but also indicate that the most galaxies are moving away from other galaxies. This hints at us that the universe is possibly expanding at every point.
However, it is important to note that these observations cannot stand on their own and prove that the universe is expanding. You'll need to take help from general relativity to conclude that the distant galaxies are moving away from us faster than light, or in other words, the universe is expanding.
The cosmic microwave background radiation and the cosmological redshift-distance relation are together regarded as the best available evidence for the Big Bang theory. Measurements of the CMB have made the inflationary Big Bang theory the Standard Model of Cosmology.
The cosmological redshift has played a very important role in our understanding of the universe.