first, i’ve been to the vatican and didnt see this particular mosaic anywhere that i went in the PAPAL tombs under St Peters, which are the only tombs accessable to the public and take up quite an extensive area under the basillica. however, simply because i do not recall seing this particular section of a particular mosaic, does not mean it doesnt exist.
HOWEVER, i see nothing, absolutely nothing in that very small piece of an obviously large mosaic which points to either mithraism or the “sun god.” for starters, the portion of the large disk shown brown on the side is not likely a communion host, based on the size and coloration. a host would be shown in white, and you dont see them very often nor with black design on the edge in classic mosaics. It is more likely a halo on a much larger figure, like Jesus. that would make the very small character shown to be either an angel or a saint… most likely an angel, based on the wings, since wings are clearly lacking from the description of the sun god.
Further, the mosaics in the vatican were not produced at a time when pagan rome still existed. these would have come much later than the creation of the church. as such it is reasonable to presume that mithraism and other pagan roman religions had long faded before the creation of this piece, which makes the placement of the roman sun god into the work even less probable.