That might be a little idiosyncratic, but the decision on force_embed was so we could control the layouts in the theme based on whether the initial launch arrived for a full course or an activity within a course. If a course design is using specific Moodle
activities within canvas, we strip out all navigation for students and add minimal navigation for teachers so they can still easily manage their course; if the students are to launch into a course and click around different
activities, then we need to leave navigation intact. We also make different
postmessage calls against canvas depending on which of those two design options are in use to maximize space for the moodle-containing iframe and remove potentially confusing navigation controls in Canvas.
$Canvas.user.loginId
We needed the canonical username for user account creation instead of the obfuscated LTI sub username so that we can launch LTI activities from the Moodle LTI tool with the same user that the platform would use. (For example, so they see their video collection in our video management system). The lis_person_sourcedid is provided with sync_members data from the NRPS, but not with launch data (Moodle's mod_lti sends it in claim at launch, so great job, HQ).
$com.instructure.User.sectionNames
We needed to sync SIS-generated section names in Canvas with Moodle groups.
$Canvas.user.sisIntegrationId
This other id was needed for a library-related LTI integration we needed to support in the tool.
$Canvas.api.baseUrl
$Canvas.course.id
$Canvas.moduleItem.id
These are used for a local plugin I wrote to, among other things, route 403 requests to the launch point that gets the user closest to that requested context so that auth_lti acts like a real authentication plugin if someone follows a direct link to a resource on the LTI tool instead of arriving from the platform able to authenticate. baseurl was needed since, as you discovered, the app registration doesn't use the vanity urls for the instance of canvas, and I thought this preferable to parsing it from the NPRS or AGS urls, if provided.