You don't want that. You could easily have a database blown with malicious requests that result in 404 or 403 or whatever error. At least do not mix it into the Piwigo database, use a separate database instead. In any case, it wouldn't be a job for a Piwigo plugin because if there is an Apache error then Piwigo isn't even involved. However, I think it's a bad idea.

If you want an overview of server requests and errors, there are plenty of tools that analyze the server logs.

If it is only for MySQL errors that result from Piwigo requests, situation may be different. But for that all request would have to go through some API that a plugin could intercept. I doubt that's the case.