“All of the seven days of the milluim Moshe served as the Kohen Gadol but the Shekhinah did not come to rest on the Mishkan because of his actions. However, when Aharon wore the garments of the Kohen Gadol and performed the Service, the Shekhinah did rest on the Mishkan because of his actions (Y. Yoma 1:1 2b).”
According to this teaching, although Moses did perform (Exodus 29) services in the Beth Mikdash due to his special status, he did not wear the garments of the Kohen Gaodol. Only Aharon who was the Kohen Gadol was permitted to do so.
The fact that the Shekhina did descend when Moshe performed the Service seems to suggest that he did not have the status of a Kohen Gadol, a point of dispute in Bavli Zevachim 102a.