The WordPress activity log is not deleted when you deactivate or uninstall the plugin.
When you disable or uninstall the WP Activity Log plugin the WordPress activity log is not deleted. So when the plugin is re-installed, even if it is a different version you will still be able to access the same activity log and the plugin settings will be retained.
Note: To delete the WordPress activity log and plugin settings from your website upon uninstall enable the option Remove data on uninstall from the plugin’s advanced settings tab.
Can I purge the WordPress security log to start afresh?
If you want to start afresh, you can purge the WordPress security activity log by navigating to the plugin’s settings, click on the Advanced Settings tab and click the Purge button next to the Purge Activity Log setting. You can also reset the plugin settings to default from the setting Reset Settings. Both settings are highlighted in the below screenshot.