Hello Layft Greater!
My point was that OSM types or statuses are about truth on the ground and it's not always equal to government classification. Gov classification is just one of the sources, but only one for OSM.
And this principle is applied in many countries like Greece osm.wiki/Greece#Highways_in_Greece (primary is not only for roads with gov status 2, but also city-level link roads) or in the US (see osm.wiki/Tag:highway%3Dprimary#International_equivalence ) and so on.
And also this common OSM definition is already applied in Cyprus (like E323 and E207 and others in Larnaca, or many E* in Nicosia like E1003, E928, E115 etc.). Even Cyprus government maps show E* roads as primary (for example E113 on https://eservices.dls.moi.gov.cy/img/staticthumbnails/Lemesos_East_Eng.png and many others).
So these are the reasons to mark these roads as primary too, as they have a lot of traffic and are used as city-level connecting roads (and so not to just copy gov statuses). And I hope it's in line with the harmony of other Cyprus road statuses :)

lets discuss in case of any advises