Screeching when shifting (manual transmission) - BMW 328i

I’ve got a 1996 BMW 328i manual. It has 175k miles. I purchased the car about a year ago. Several weeks ago, I began hearing a screeching noise when shifting when the car is cold.

The screeching happens when you let the clutch out when going into gear. It happens much more frequently when very little throttle is used. If you shift it harder, it is less likely to make the noise.

If it starts making the noise, you have to shift several times for it to go away. It’ll still make the noise while in gear at that point.

When the car is driven for about 10 minutes, it never makes the noise afterward, until the car cools down completely overnight.

The clutch does not appear to be slipping at all, and once a gear is engaged, it does not have any issues staying in gear.

What is my car’s issue?

Perhaps a throwout bearing, perhaps a glazed clutchplate, perhaps a pressure plate. Perhaps even a pilot bearing.