I hear four sounds, three different . Dont know which is of concern.The first two similar sounds?
Is the tape rewinding slower now?
Does Fast Forward also make the same new noise.
You might try a stethoscope to localize the cause. Works well for automobile troubleshooting.

I have seen VCR transport that have trouble with certain tapes due to tape cassette housing being broken.
You probably have eliminated that possibility.
My gut feeling is that you are not going to hurt your VCR due to this.
In the old (ancient) days I remember VCR that would unload the tape when commanding rewind or FF first before moving the tape and leave it on the head for cue and review. all my newer ( relatively newer) VCR now rewind and fast forward with the tape on the head. I dont like that.
I picked up a tape re winder a while back. It was just a couple of bucks at the second hand store. I see them for sale all the time there (thats one nice thing about having an archaic hobby!).

I like it especially since my all my VCR drag the tape over the head on rewind.