Is there a way to test the mat without having to pay 160 USD? a DIY monitor maybe?
Sure. Check eBay if you're after a ready-made product (used or Chinese clone), or even look for circuit designs online & build one yourself (impedance monitor that indicates high, low, pass; add an audible signal if you want if it's not within pass range <750k - 10M is what they're commonly designed for Pass range IIRC>).
A multimeter would work fine. The resistance between one of the snaps on the mat and ground should be just a few megohms. If you wanted a dedicated visual tester, a simple LED circuit with a high impedance input should do the job.
If GoatZero was to do so each time before starting work on the bench, absolutely.
But the way I read that post (forgetfulness of what's plugged into a mains socket or not), it seemed a continuous monitor would help with this issue better than a spot check method/device (still has limits, such as needing a working battery). One with an audible alert would be better than just an LED indicator IMHO, as the sound is a "hey, you unplugged the ground" reminder.