Not only are we without proof that anyone in authority during the Galileo Affair thought the earth was a globe, there is some proof none of them were convinced earth was a globe.
From Galileo historian AA Martinez from the book Burned Alive
Pg 135 and 136
Furthermore, Bellarmine reasserted traditional interpretations of scriptures. So he denied the Earth’s motion. In 1611 Bellarmine quoted Psalm 103:5 from the Latin Vulgate, that God established the Earth on its foundations, it cannot be moved forever and ever’. Bellarmine commented that God put Earth in the centre of the world, and that its ‘weight rests on its eternal stability’.159 He also 136 burned alive quoted Psalm 118:8, that God ‘established the Earth and permanently’. Bellarmine explained this phrase: ‘it almost says that you [God] established the Earth immovable, and it always remains immobile.’ He added: ‘God ordained, on the contrary, that heaven or the Sun move always.’160 These statements matter, because they show Bellarmine truly believed that the Earth does not move. So, its motion was not one of the questions he sent to the Collegio Romano. He only asked about the telescopic phenomena Galileo had described. The Earth’s motion had been censured by the consultors of the Inquisition in the works of Bruno. Strangely, historians hardly ever mention this key point when discussing Galileo.
Here we see that not only did Bellarmine not believe earth moves, he believed God established the earth on its foundations. No glober even remotely suggests earth has foundations as it's hanging or twirling around in space. Bellarmine and the Pope also agreed that earth is covered by the firmament with water above the firmament. No outer space.
The following is found in the sixth argument against Galileo which led to the condemnation of heliocentric theory.
Sixth Argument
According to Genesis 1, there are waters in heaven above the firmament and beneath it. ‘Therefore the Earth’s Water is not contained only in the solidity of the Earth, and consequently the natural place of the Earth is not the centre, but possibly, outside it and carried in circular motion in a Great Orb.’
More from Martinez
pg217
Antipodes
Inchofer cited Lactantius and Augustine for having criticized the theory of the antipodes. In City of God, Augustine denied the antipodes as a ‘fable’ that had not been proved, because, he said, even if the Earth indeed were spherical, one would have to prove that it has lands throughout, not just bare waters, plus, one would have to prove that there were people there, and descended from Adam.224 Augustine preferred biblical and historical evidence over scientific conjectures. Similarly, Inchofer argued that the Earth’s motion was imaginary and false.
Obviously, the theologian, Inchofer, who summed up the entire Affair, as well as the thoughts of the Pope and Bellarmine, showed they were not convinced earth is a globe.