Where is the documentation of these ids?

It should probably be better documented. Currently it's only mentioned on the documentation of {{senseid}}.

I understand what is written there but – yet not understanding the template/module structure of the English Wiktionary – have to ask: Why is it written there and what speaks against adding the text to Category:Morphology templates (or a higher place from which on that technique has an influence)? You should probably specify on the appropriate place (depending on what the “such” templates are that are talked about at the T:senseid) that there is an extra argument that can be assigned.

The documentation of {{affix}}, {{suffix}} and such should definitely make mention of this feature. Perhaps they could, at the very least, include a link to the section of {{senseid}}'s documentation.