Sitting alone in a loud cafeteria takes more nerve than blending in at the crowded table.

Blending in is the easy move and everybody knows it. You sit where you are tolerated, laugh at things that are not funny, and nothing bad happens to you. Being visible with no cover is a different thing entirely, and most people never build the nerve for it. That is separate from being left out, and it is not something you owe anyone proof of.

If you already eat alone some days, you can stop treating it as evidence about you. Bring something to read, look up sometimes, let the room be loud. And if you would rather have company, one honest invitation to one person usually does it.