Hi,
There is something not okay with that installation path, that within the error message. The plugin path in the message is ‘/ajax-search-pro.bak/’, while it should be ‘/ajax-search-pro/’. Please make sure to disable, and remove the plugin via the plugin editor screen, as well as check if there is any directory with the name ‘ajax-search-pro’ within the ‘wp-content/plugins/’ folder and remove that as well.
Either the extraction process failed, or there might be an archivation system active on your site, that may have made a back-up copy of the folder for some reason.
Once everything is removed, try uploading and installing the plugin again via the plugin manager. It should work.