My multi pilot IR had lapsed so had to do the renewal flight test (departure, airway, 2 x approaches, GA). Only thing cross credited I guess was that there was no minimum training required before being allowed to do the test. I did do some training so forms were a Course Completion Certificate, and Examiners Report (I can't remember the numbers...).
As I mentioned, once the Licence was reissued with the renewed rating on it, the portal didn't show it straight away. I guess the law requires it that way; the definitive document being the paper licence rather than their database. I guess It would be too simple if one could be informed by email that the rating had been issued and the database updated, then one could then check the database and print a copy of the licence.
Has your licence been reissued with the IR-SP-SE on it?