I’m not in CA so don’t know how their standard lease is structured. But from the section you included, it sounds like when you moved in, they should have prorated your rent and only charged you for the rent from 8/8 to end of the month.
If you paid full rent for the first month of August and every month after, then you may have a case, but I wouldn’t assume that a notice on 4/3 would allow you to vacate 5/3 unless that’s how CA lease is structured e.g. if your lease has a clause that any notice must be given before the first of the month, etc. then April 3 May be too late On the other hand, your landlord may be more flexible as he’s selling the property.