How do they track that? Is there a log book where someone has to write to?

"Observed EMP555 step on loop heat pipe. Conducted visual inspection of the affected area; no damage found, pipe remains nominal."

I'm sure they take detailed close out photos and likely video of the entire handling process.

“Measurements taking of the person: foot and shoe weight, total weight including clothing, height and leg length, estimated velocity of travel at time, estimated duration of load”

Since it went into space with the stepped-on part, clearly nobody DID write it up.

They really don't care. If the satellite blows up or fails, they get to build another.

I didn't but that's the case. More likely there was a limited chance to evaluate the issue and something like they had a limited time launch window, no replacement ready and it tested good. "Just put a little butter on it, it's fine".