I have a 2007 Pontiac G5 with a 5-speed manual (Getrag F23 if you're curious) and about 145k miles.
This problem has been ongoing for a couple years now but is progressively getting worse.
Sometimes when I shift into first while stopped, like at a traffic signal or stop sign, the gearbox will make a horrible grinding noise. About 50% of the time I encounter the grinding, the car's electronics also freak out - the speedometer shoots up to 70mph or so (mind you, I'm stopped), the stereo will momentarily become louder, and the engine speed will drop then go back to idle. In rare occasions, the car will stall when this happens, though it doesn't lurch forward like it would if I hadn't let off the clutch properly.
Here is a video I captured with my dashcam of it happening: https://youtu.be/7-3PYX9f66U
You can clearly hear the grinding, followed by me having to start the car after it stalls.
I have tried researching this online but have not have not found any solutions. I have also ensured that I am fully depressing the clutch and waiting a couple seconds after doing so to shift.
This does not occur in any other gear, especially while moving (though I have experienced the electrical phenomenon a couple times when shifting into reverse). The clutch and throwout bearing were both replaced about 18k miles ago, but the problem occurred before then and persisted afterwards.
Any help would be much appreciated.