Vbi is the barrier voltage and is constant, whether a source is connected or not. The source will not reduce the barrier voltage, it will reduce the junction voltage Vj = Vbi -Vbe. Vj = Vbi only when Vbe = 0. I don't have the same Sedra book you have.
vbi is not the barrier voltage. The source reduces the barrier voltage, just as Sedra and Smith says. It's in the book, you only have to read it. Also see Gray and Mayer.
Barrier or built-in voltage is fine. The junction voltage is the result of subtracting Vbe from Vbi. We appear to agree on that.
Also, the reduction in barrier voltage is equal to vbe, This might seem trival, but the ramification is if you control the barrier voltage, then you control vbe. And Sedra and Smith shows that current controls barrier voltage by neutralizing charge in the depletion region. If you need an equation, vbe = vt*ln(Ie/Is), also given in S&S
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