You didn't say what $\lambda_n$ and $\lambda_r$ are, I've assumed they're the real pole positions.

(14.10.3) and (14.10.4) look OK, and I think (14.10.2) is defining $\omega_d$ to be similar to the under-damped case (where it would be $\sqrt{1-\zeta^2}$.

It's not so obvious what (14.10.1) (and (14.10.5), which can be derived from (14.10.1)) is for.

What are either over-damped $\omega_d$ values supposed to tell us? For the case with no zeros, the response is either approximately that of a double pole, or dominated by the slow pole. We can use the $\lambda$ values for that.

If I apply these equations to the real poles in your example, I don't get the values for the two definitions of $\omega_d$ to match (perhaps I made an error?).

def overdamped(ln, lr):
    if not ln.imag == 0 and lr.imag == 0:
        raise ValueError('poles must be real')
    if not lr < ln < 0:
        raise ValueError('require lr<ln<0')
    
    wn = (ln * lr) ** 0.5
    zeta = -(ln + lr) / 2 / wn

    wnd1 = wn * (zeta**2 - 1)
    wnd2 = 0.5 * (ln - lr)
    print(f'{wn=:.4f}, {zeta=:.4f}, {wnd1=:.4f}, {wnd2=:.4f}')

overdamped(-31.67, -140.8)
overdamped(-2.121, -2.983)

gives

wn=66.7768, zeta=1.2914, wnd1=44.5865, wnd2=54.5650
wn=2.5153, zeta=1.0146, wnd1=0.0739, wnd2=0.4310

control.damp(sys) #839

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