A lot of people panic-do masters. I don’t know anyone who has voluntarily done a masters because they want to do a PhD, everyone i know who has done a masters has done one because they can’t find employment.
One of my friends did a masters, was applying to jobs during his masters, but didn’t get relevant employment (an internship, not a proper job) until 6 months after graduating his masters - despite going to a good university and good CV. so, he was searching for 1.5 years, and he is still trying to find a long term job.
For my other friends, anywhere from 9-12 months seems to be the norm. Don’t worry, 3 months is a relatively short time in the grand scheme of things, and if you’re able to get something within 3 months, you’re definitely on the luckier end of the scale. Those figures universities post are the most misleading things ever, but hopefully you find something very soon.
Best of luck, and P.S: perhaps targeting internships as opposed to grad jobs may be better if you said you don’t have much prior experience.