I found Proventus Avenicci (steward to Jarl Balgruuf of Whiterun) in Solitude but I can’t ask him to buy Breezehome in Whiterun. What do I do?
You'd have to talk to Brill instead. At that point in your game, he has replaced Proventus Avenicci as the steward of Dragonsreach in Whiterun. Since Proventus Avenicci is in Solitude, that means that the Stormcloaks are in control of Whiterun.
As per the UESP wiki "Proventus Avenicci" article:
If the Stormcloaks take over Whiterun, [Proventus Avenicci] will move to Solitude. There he can be found in the basement of the Blue Palace, but he will not sell any property or upgrades. These options are moved to Brill, the steward who replaces him. He can be found in the Great Porch area of Dragonsreach.
UESP wiki "Brill" article:
[Brill] will replace Proventus Avenicci as the steward of Dragonsreach if and when the Stormcloaks conquer Whiterun, which leaves Vignar as the new jarl. Like Avenicci, he will sell Breezehome and its furnishings...