The Pope -- Bishop of Rome. While his concerns are mainly with the Universal Church, the Pope remains of course the Bishop of Rome, which is the central reason of why he is the Pastor of the Universal Church in the first place.
But since for many centuries, they have been so busy with the Church outside the City, they have for many centuries kept a Cardinal-Vicar, who administer the diocese.
Also for many decades, especially since Rome became once again a bustling modern metropolis, the central area of the City (which includes most of what the ancient, the modern, and the pilgrims and tourists identify as Rome proper) has been administered as a whole: the map below, from the pontificate of Benedict XVI, identifies this area, the Settore Centro, in red (the Vatican itself appears in yellow). The exact limits at the time had been defined by John Paul II.
We know that that is what happened with the disgraceful motu proprio "Traditionis custodes", mostly ghost-authored by a radical liturgist called Andrea Grillo. The same happened with the organization of historic Rome; Italian page Silere non possum explains:
To understand the scope of today’s decision, one must return to that 2024 Motu Proprio, drafted - as Silere non possum repeatedly denounced - on the basis of the ideas and pressures of Renato Tarantelli, the vice–vicegerent of the Diocese of Rome. There had been no real consultation with parish priests, no communal discernment, no dialogue with those living the daily pastoral work in the neighborhoods. Only an ideological framework, a reform designed at a desk, as if Rome were a model to be reshaped according to the theories of some improvised urban planner.
...Francis’s measure dismantled the Central Sector, scattering its Prefectures among the four cardinal sectors. The reform was presented as a “synodal” act, the fruit of “numerous interventions” and “requests already made.” Here honesty is required: those requests came from nowhere except Tarantelli’s desk. The parishes, invoked as if they had participated, knew nothing about it. The number of priests heard: zero. The overwhelming majority of Roman presbyters learned everything after the fact and were left stunned. (source)
