Here's Christ as Sol Invictus in a ceiling Mosaic at the Vatican grottos. This was common in early Christian iconography.

Church commonly appropriated varous pagan symbolism to displace the pagan meaning and substitute them with a Christian one. This is one of the chief complaints of the Prots against the Catholic Church, that it became paganized.
https://catholicunderthehood.com/2016/03/11/328-a-history-of-the-catholic-church-sol-invictus/
The link you provided only shows that one example, claiming it is Jesus and provides many links to coins with the Roman sun god Sol Invictus and Apollo.
I can't find any other depictions of Jesus as the Sol Invictus.
There seems to be dispute over whether that depiction in the tomb is of Jesus or of Helios, the Roman Sun God also known as Apollo or Mithras and more.
The popularly named "Tomb of the Julii" (Mausoleum "M") survives in the Vatican Necropolis beneath St. Peter's Basilica. The serendipitous discovery near the crypt has a vaulted ceiling bearing a mosaic depicting Helios (Roman Sol Invictus) with an aureole riding in his chariot, within a framing of rinceaux of vine leaves. The mosaic is dated to the late 3rd century to early 4th century. Other mosaics in this tomb depicting Jonah and the whale, the good shepherd carrying a lamb (the kriophoros motif), and fishermen have encouraged its interpretation as a Christian tomb.This tomb was first discovered in 1574 AD when workmen accidentally broke through the ceiling while conducting some floor alterations in the basilica. The inside was briefly explored and docuмented before the opening was sealed over once more.[1]
https://en.wikipedia.org/wiki/Tomb_of_the_Julii
And here
The charioteer in the mosaic of Mausoleum M has been interpreted by some as Christ. Clement of Alexandria had spoken of Christ driving his chariot across the sky.[54] This interpretation is doubted by others: "Only the cross-shaped nimbus makes the Christian significance apparent",[55] and the figure is seen by some simply as a representation of the Sun with no explicit religious reference whatever, pagan or Christian.[56][11]: 567–578
For more the Cult of Sol Invictus see the rest of this article:
https://en.wikipedia.org/wiki/Sol_Invictus
So it appears that St Clement spoke of Christ and His chariot in the sky, but that is different from calling Jesus the Sol Invictus.
It's also different from depicting Jesus as the center of the Heliocentric model with earth revolving around the sun and the earth spinning on the axis of the cross.
I've never heard of that before. Have you?
Do you know of any saints or Church Fathers or popes that call Jesus the Sol Invictus?
Do you know of any who have depicted Jesus as the heliocentric sun with the earth rotating around him and spinning on the cross?
Is that found in Tradition?
Anyway, the contemporary understanding of Sol Invictus seems to be that he is Lucifer:
THE IMAGE OF THE BEAST
In Luciferian circles,. Lucifer is the Sol Invictus, in direct competition to the Son of GOD, Jesus. Christ. ~The Church Age. BABYLONIA. MEDO-PERSIA. GRECIA.
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