He is certainly the patriarch or head of the Latin Church. The title “Patriarch of the West” has only been periodically used by the popes - it isn’t like he suddenly dropped it after centuries of consistent use. It was removed from the Annuario Pontificio in 2006, but it had only been introduced to that particular list of titles in the mid-1800s in the first place… Patriarch of the West is vague and doesn’t reflect the current reality of the Latin Church.
As has been pointed out before, legally in canon law, the Church sui iuris to which the 2000+ dioceses that worship prmarily according to the Roman Rite belong is the Latin Church…the Roman Church, in legal Church documents, almost always means the Diocese of Rome - not the Latin Church at large. There are other Rites that also belong to the Latin Church that are not Roman (eg. Ambrosian). I am a member of the Latin Church who worships according to the Roman Rite…