In whose honor did Aharon wear the Bigdei Kehunah?
Ramban #2 (according to Kabalah): They should manufacture Begadim for Aharon to wear in honor of the G-d who dwells in their midst and who is the glory of their strength. 3 Also, it is to glorify the Beis ha'Mikdash, the location of Hashem's Feet and which is honored with the Kavod of Hashem. 4
Seforno: He wore the Bigdei Kehunah in honor of Hashem, in whose service he wore them.
See Ramban, who cites proofs of this with regard to most of the Kohen Gadol's Begadim with many Pesukin from Tanach in support. He also explains that this is why Ya'akov made Yosef a Kesones Tashbeitz (equivalent to the tunic that the Kohanim wore - as the Ramban explained in Shemos 25:18).
And the Torah use the same expression later, in Pasuk 40, in connection with the Begadim of the Kohanim Hedyotim.
What are the connotations of "Tif'eres"?
Seforno: Aharon struck awe upon whoever was in his vicinity, all of whom were his Talmidim, whose names he wore on his heart and on his shoulders. 1
Targum Onkelos and Targum Yonasan: It has connotations of praise.
On the stones of the Choshen and the Eifod, respectively.
If the Begadim of the Kohen Gadol were designated for Aharon and his descendents, what did Moshe wear when he served in the capacity of Kohen Gadol during the seven days of inauguration?
Rashi (Avodah Zarah, 34a): Since these clothes were specifically designated for Aharon, Moshe was a Zar regarding them and was not permitted to wear them. He served as Kohen Gadol by Divine command, and no mention is made of specific clothes as far as he was concerned. In fact, he wore a white cloak. 1
Much like the Kittel that we wear at the Seider and on Yom Kipur.