As you mentioned, the updates tab does provide a record of deletion, and if you didn't want to go trawling through all the projects and tasks for that, you could run a journal entry report looking to see whether anything was outright deleted. If you are an admin and on top of your recycle bin stuff, you can also quickly check your bin for deleted issues. Those get recycled after 30 days so I will leave you to make your peace with it.
For issues converted to a task or project, those immediately disappear leaving no trace except for the converted request originator name. So for these you might be able to run a report looking for tasks (or projects?) filtering for where the converted request ID is blank and the converted request originator ID is not blank.
