How do I repair this rot/insect damage on my wall plate?
Pacific Northwest here Corvallis/ Springfield resident for 35 years , I don't see any evidence of ants, termites or beetles our areas chewing pests, it looks more like a fungus or dry rot but is very limited , I would take a screwdriver and press to see if the damage is only on the surface if the screwdriver doesn’t go far it’s only surface damage and a fungicide then a wood treatment to harden and seal the surface should be used. I have found homes that have used the wood Treatment on spongy dry rot , the area sealed and it passed inspection but was noted as a concern, I would probably shim the stud but nothing other than that is really needed from the photo, I might leave it open for a few weeks to see if you do have a small leak  and any leaks would need to be fixed but after treating the wood with a fungicide and adding a shim or 2 , I would probably button it up once I was sure there are no leaks into that area if the wood is solid.

I do not believe it is pest based because in all 3 of our normal pests they chew channels and holes not just surface damage that I see. Do this is why I would treat the wood possibly saturate with a hardner based on the screwdriver test.