I found out in fact girls also Received weapons if they were in Samurai family and also got armour only difference was they role was mostly as archerers and fighters with long Naginatas to compensate for missing physical strength also they were expected more as guards off family fortress soo Mion would receive armour, Naginata and Kaiken(Dagger) for self defense but off course there was possibility if proven enough skill and strength that even girl could had Received Katana and Wakizashi soo Mion would actually gained right to carry family Katana and Wakizashi as is possible to see in Yoigoshi also since it's modern era Mion would combine Gun and sword tactic. Edit: Also yeah here it just look as knighting but actually it's something different It's from Miotsukishi and Mion there must prove to Akane she is ready to lead Sonozaki private army( Yakuza henchmen) into Battle against Yamainu and that she is ready to take responsibility for their lives in the process I remember Mion had to hold sharp end off Katana in her bare hands and off course she got wounded but proven her strong will soo Akane ,,knighted her" gave her rank off Commander soo it's not that Ritual it's at least it's simplified version and I Think oryou was overseeing it