You are absolutely correct about sideslip (beta) as it factors into dihedral. In shallow turn, as soon as the vectors split there's a weight factor that causes sideslip toward the low wing. The sideslip causes a lift imbalance due to greater aoa on the low wing in a shallow bank that dihedral tends to counter by returning the wings to level flight.
This is especially a factor in shallow turn if dihedral is present and dampens out as medium banks are introduced and gives way to other factors as deep bank is approached and acheived.
The bottom line is that the individual physics involved in turns vary in intensity and individual dominance depending on specific design all through the normal bank range of a specific aircraft.
DH