u/DDESTRUCTOTRON

First pic shows the back of the bathroom mirror cabinet. It's made of compressed wood. The red circles are where the threaded inserts screw into the back panel of the cabinet. The inserts fit fine into the back panel.

Second pic is a closer look at one of the little metal threaded inserts after I unscrewed it from the inside of the cabinet. The mirror came with screws for the inserts, but they're way too skinny for the threads on the inserts. I've tried a ton of different screw sizes and asked for help at the hardware store a couple of times after bringing the insert with me, but still haven't been able to find the right kind of screw that would fit the threads of the inserts. I'm beginning to think these are custom or something.

I already have holes measured and drilled into my bathroom wall where this cabinet is going to be mounted, but I can't actually mount this thing without screws that fit.

How can I mount this? Should I either try to find screws that fit the threads on the inserts, or is there a way I can replace the inserts with something else?

There is a horizontal stud in the wall going across where the top screws of the cabinet would be mounted, so at least it's going to hang off of something sturdy. The bottom screws are just going into drywall, but I already have drywall anchors in those holes. All of the holes in my wall are sealed shut with painters tape until I can figure this out. Any help is appreciated, thank you.