My external hard drive won't show up in the disk utility

Try a different port. At this point I'd suspect a bad adapter. How does the drive function on a different computer? If it works on a different computer that's a clue your problem may not be the drive at all.

You have effectively eliminated the drive and adapter as having problems; your Mac is the problem. As to next step, I'll defer to better minds.

Did you try flipping the USB-A to USB-C adapter over? Some are direction sensitive and will only connect in one orientation.

Did you try another drive? Perhaps the drive is drawing too much current and keeps disconnecting. I have had this issue before.

All computers are not the same regardless of spec.