The basic, and disappointing, answer is that we don't really know : there were not really a defined set of imperial regalia at this point (and even if there were, with the endless successions and coups since the mid-Vth century, they would have been in serious risk of being lost or separated already).
Even as imperial ornaments were sent back by Anastasius to Theoderic in 497, there is no description of them, although they are considered imperial and not just honorific.

Jonathan J.Arnold proposes to consider the insignias sent by Anastasius to have included

all the trappings of imperial rule sent to the East in 476: an eagle- or cross-adorned sceptre, a crown or diadem, bejewelled slippers, lances, and purple and gold-embroidered robes.

For what mattered Constantinople, it would have marked the different status of Theodoric as some sort of vice-emperor for the West, compared to the insignias and honors given to the other Barbarian kings, technically imperial clients. That said, it never prevented Clovis to bear a purple mantle, or his son Theuderic to coin himself dressed as a Roman emperor), so maybe Jordanes isn't as wrong as Arnold proposes saying Theodoric had royal clothing : Barbarian kings tended by the VIth century to copy Byzantine court usages.
Now it's true that clothes sent by Constantinople, especially if they were elaborated tablions or epigonations, they might have been much more richly decorated and much more obviously representative of late imperial insignias sent by Odoacer and recieved back by Theodoric.

Some additional insignias proper to the IVth and early Vth might have been used specifically by the late emperors : an orbis mundi, an elaborated cross-like or circular (and detailed) broach, ...