Something is off because the “Add New Media” shouldn’t be having errors like that. So lets do some basic troubleshooting to see if we can identify where the issue is. Disable all plugins and turn on a default WordPress theme (twentyfifteen). Test the site. Can you upload media successfully? If you still get an error message this tells us the issue is between WordPress and the server. I would check file permissions at this point and make sure that whatever user account WordPress has on the server that it has write access to the “wp-content” directory. Learn more about permissions here: https://codex.www.ads-software.com/Changing_File_Permissions
But if there’s no issues when using a default WordPress set up, then the issue is with either the theme and/or plugins. So lets test that by re-enabling your custom theme. Test to see if uploading and attaching media works correctly. If yes, great, your theme is good to go. If not, time to contact the theme developer and let them know about the issue. Make sure to provide the developer with as much detail about your WordPress setup as possible so they can try and recreate the issue.
Now if the custom theme works fine, that tells us the issue might be in a plugin. So we’ll now re-enable plugins, one at a time, testing the Add New media functionality after we re-eneable a plugin. If it works, great, move on to the next plugin. If at any point you see the issue, note which of the plugins you last enabled and contact the plugin developer and let them know about the issue. Again, provide as much detail about your WordPress setup as possible so they can best recreate the issue.
Hopefully by the end of this process you’ll have a better understanding where the problem is and can get it fixed. If despite these steps the issue still persists, you may need to work with your hosting service to identify the issue (it may be how the server is configured).
Also, you may want to try a manual update of WordPress: download the latest version of WordPress to your desktop, unzip, and then re-upload via FTP/SFTP to the server and replace the existing WordPress files **except the ‘uploads’ folder and ‘wp-config.php’ file**. Sometimes automatic updates don’t completely work on the rare occasion and a manual update can help fix things.