I note that the text is talking about the faces and feet of the Seraphim. יְכַסֶּ֣ה פָנָ֗יו וּבִשְׁתַּ֛יִם יְכַסֶּ֥ה רַגְלָ֖יו וּבִשְׁתַּ֥יִם יְעוֹפֵֽף: The Hebrew commentaries have some interesting remarks about this. See for example https://www.chabad.org/library/bible_cdo/aid/15937/jewish/Chapter-6.htm#showrashi=true
Seraphim stood above: in heaven. for Him: i.e., to serve him, and so
does Jonathan render: Holy servants are on high before Him. with two
he would cover his face: so as not to look toward the Shechinah. and
with two he would cover his feet: for modesty, so as not to bare his
entire body before his Creator. And in Tanhuma (Emor 8), I saw that
the feet were covered because they are like the sole of the foot of a
calf, in order not to remind Israel of the sin of the golden calf.
and with two he would fly: And with two he would serve [from Targum
καὶ Σεραφὶv εἱστήκεισαν κύκλῳ αὐτοῦ, ἓξ πτέρυγες τῷ ἑνὶ καὶ ἓξ πτέρυγες τῷ ἑνί, καὶ ταῖς μὲν δυσὶ κατεκάλυπτον τὸ πρόσωπον, ταῖς δὲ δυσὶ κατεκάλυπτον τοὺς πόδας καὶ ταῖς δυσὶν ἐπέταντο.
And seraphim stood round about him: six wings to the one and six wings to the other: with the first two [they] covered up the face/front; with the second two they covered the feet and with the third two they flew.
Note that the Greek does not explicitly say whose feet and face was covered. However, the fact that they used two for flying implies it is probably their own especially in view of the Targum comments.