Could Cognate also work for the rhyme namespace? Or would it be more something for the phase with interwiki links in Wikidata?
That looks too complicated for Cognates.
You would need a template for each and every language, e.g.
- Annexe:Rimes en %FR:LANG% en \%RHYME%\
And not only a template, but also a list of all the languages in all the languages.
That's also assuming there is no special cases in a given language, e.g. one would write rhyme in /ir/, others /iʁ/ for the exact same rhyme.
That's a lot of work compared to keeping the interwikis.