Hi
I'll have a go at quickly summarising some of this as follows:
Authentication integration
A Xerte install can be set up to use a variety of authentication methods and although SSO via saml2 is more common these days you can also use Moodle authentication so that when a user visits the Xerte address they are redirected to login to Moodle first and then redirected back to Xerte or automatically logged in if already logged in the Xerte. How to set this up is documented in a file named moodle_integration_readme.txt inside the documentation folder of the Xerte download.
Content integration
Any Xerte project you create has options for sharing which include:
A public link that you can put anywhere in Moodle that you can add a hyperlink. So the benefit is that a public project can be added to any number of Moodle courses and resources but also shared directly outside of Moodle and any changes to the project in Xerte are automatically included in all those places.
A link that requires login - so the same as above but the user has to login to the Xerte install first and if set up as Moodle authentication that means Moodle.
Export as deployment and import and extract the zip in Moodle and link to the index page. Means the project is now independent of the Xerte install and available wherever you put it in Moodle.
Export as SCORM - as above but includes SCORM tracking.
LTI 1.3 integration
Once this is set up between your Moodle and Xerte installations then anyone who creates a project in Xerte can add the LTI link to any number of Moodle courses. This restricts access to the project to those courses and also stores grades in the Moodle gradebook (if required) but at the same time allows the project authors to update the project and add new content to it without having to export or import as they have to do with SCORM.
Also one single Xerte install can be set up with LTI 1.3 integration with any number of separate Moodle installs as well as other LMS like Sakai, Blackboard, Brightspace, Canvas etc etc. A key point here is that if you ever change VLE/LMS you don't lose any of your Xerte content and can use the same content in any number of LTI 1.3 compatible applications.
LTI & xAPI integration
This requires an LRS but with that and the LTI 1.3 integration set up you get all the benefits of LTI together with xAPI tracking and automatic dashboard that you can view in Xerte but also add to Moodle for learners to view their own dashboards.
There are some very old videos on YouTube about using Xerte with Moodle that I created but so long ago now (14 years!) that they probably aren't a good thing to refer to now although the principles remain valid.
You will however find recordings of conference presentations about LTI and xAPI use here on
xerte.org.uk/index.php/en/news/blog/158-videos and also our Xerte 2023 conference resource
xot.xerte.org.uk/play_450#programme
Many of those sessions may not mention a specific VLE/LMS but will often show how the person/organisation is using Xerte with their VLE/LMS and the same principles would apply to Moodle even if that isn't what they are using. There are also numerous sessions that cover the wider benefits of using Xerte as well as in some cases comparisons with other tools.
HTH
Ron