I've got many different instances of moodle. Our production system will not backup LTI tool information. Here is an example of exporting an LTI tool that is configured as a pre-configured tool.
https://moodle.org/pluginfile.php/127/mod_forum/post/1722765/Gradescope%20LTI%20export.xml
You can see that the ltitype element for the tool is mostly empty. This means if we migrate to another instance of moodle, the tool doesn't get restored in any useful way. It's like this for all the external tools.
I've tried setting up LTI tools on the other instances and then created courses with those tools and backed them up and the ltitype element contains all the data you need.
So I am wondering what are possible reasons on our production system why the data doesn't get exported in the backup. Are there settings somewhere I'm missing?