The most common answer to the Sozin is 6Bc4
e6. Benko played 6Bc4
Qb6 against Fischer and that has steadily gained in popularity. Gligoric answered Fischer's 6Bc4 with 6...
Bd7 and ...g6. Black has also combined ...Bd7 with ...e6. This can occur via several move orders.
After 1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 Nc6 6. Bc4 e6 7. Be3, Golubev wrote in 2001 that "
7...Bd7!? has not been studied enough."
Ivan Cheparinov prepared a data base for Modern-Chess on the Classical Sicilian in 2022. I mostly looked at if for his analysis of the Rauzer attack, 6Bg5. I was surprised by his extensive coverage of 6.Bc4 with new material of benefit to both sides. He included all answers to 6.Bc4, including ...Bd7 lines. GM Arjun prepared a data base on the Classical Sicilian in 2024. In it, he answered 6.Bc4 with 6...Bd7. After that, he plays ...e6 or ...g6 or something else depending on white's moves.
Black can defer ...Bd7 to move 8, disguising his intentions: 6. Bc4 e6 7. Be3 a6 8. Qe2
Bd7!? 9. O-O-O b5 and black succeeds in accelerating his queen side play with reasonable chances.