Yeah no that's indefensible and the original editor in chief is nuts (google translate from the Ukrainian wikipedia page):

This is an old Ukrainian sign, which means a force aimed at destroying all the old and restoring the new. There is another version of its origin: the black sun is the period of the year when water acquires special life-giving qualities. This usually happened at night, when there was no sun, but since the nutritional properties were always associated only with it, our ancestors nicknamed this time the black sun. There is no hint of hostile ideology here, this is our Ukrainian symbol, which has a sacred meaning.

— Mark Melnyk ("Viry"), editor-in-chief of the publication

Couldn't find out when it was discontinued, the azov.press domain certainly is dysfunctional. Azov's official news feed seems to be here.

Could neither find out how official the whole thing was, either, and especially not in the crucial post-incorporation times. They might just have continued to operate independently.

Still, though: Is current-day Azov out there doing Nazi things? Ultimately that's the only question that matters. Of course from the Russian perspective yes it is according to Russian propaganda everyone opposed to Russia (and that includes being opposed to being invaded) is a Nazi.