Furu
Member
Can you get in there with a small scraper or a sharp knife edge to scrap the burnt wood? Continual sanding will distort the radius and the edges and might make it look worse.
As @Cheese said, detail scraper or card scraper.
You can get the economical version at the hardware store.
I used both types of scrapers to deal with the burn marks in a recent project with great results. Sanding wouldn't cut it.

The project is a bench called Krobo by Torbjørn Afdal
Well done!
Also, the side light is a fun one.
question — Is there supposed to be a lip around the perimeter of the benchtop? or is it a photo skew thing?