The WordPress AI Alt Text Generator Plugin comes with logging functionality that lets you see a list of the different alt text generation jobs that have been run by the plugin.
To view the logs, go to Settings > Logs
If you would like to completely disable logging or change how long logs are retained, go to Settings > Advanced.
Debug Logging
If you are experiencing issues, the plugin also comes with the ability to enable debug logging, which is more in-depth logging that includes errors. To enable this, go to Settings > Advanced and enable the Debug Mode option. Here you can also use the Log Level option to get the best logging possible for your purposes.
If ever you need to contact support with an issue, make sure to enable the debug mode first. It may give you your answer before even needing to reach out, or, at the very least, you can provide us with the log right away, so we can help you to address the issue more quickly.