This, and make sure it’s not on High Idle either. Mine sounds more like a jet when it’s in high idle, but close enough to that table saw sound you linked that I can hear a similarity.Can you verify that your exhaust brake is OFF when starting truck? If it's on, try starting it with it off.
FWIW, I would double check everything on the exhaust to make sure it’s not touching anything it’s not supposed to. The jet sound is normal for a high idle, I almost wonder if the whine of your table saw is caused by a slight vibration somewhere along the pipe.
BTW, you nailed it with the description of a table saw, I wasn’t expecting the sound clip to sound like that but I’ll be damned