The obvious problem is the lack of any grain. For that, an Exacto blade may be your best friend.

When I repaired a friend’s oak table, which had sprouted wings and few out of the back of a pickup, I scratched my head over how I was going to blend the patch.

A butt joint became a sore thumb, so I chiseled out the damage to bring the lines MORE parallel to the ones around them. Then I carved light lines in. When the stain and finish went on, the repair went to invisible, when done.