Brooks, the main reason that an SObject or SObject field wouldn't show up in the OST is that the connection user is not authorized to read those objects/fields. Please see the description of the connection-level
Ensure field read access option here:
Note that I do not recommend that option for non-DE/non-scratch orgs, so please only enable it if you're fine with IC updating the connection user's profile! But you can, of course, certainly update the user permissions explicitly via profile or permission set to ensure all of the missing objects are readable by the connection user.
If that doesn't do it, it's possible that there's something special about those objects where they aren't included in the Salesforce Metadata API responses used by IC to enumerate SObjects and fields. I can provide some diagnostic commands that you can run to help determine whether or not that's appears to be the case.
Regards,
Scott Wells