But surely minimum sink rate is only relevant when there is no power
or thrust?

I suppose so. If power were constant with airspeed, then minimum sink
would also be Vy.

It requires finding a minimum value of V*sin(theta) where theta is
the angle of climb (negative when descending).

Sounds good.

As I recall for a gliding aircraft minimum sink comes roughly at the
AoA where (Cl^(3/2)/Cd is a maximum.

I'd have to look it up to be sure, but it looks right.

This is normally at a higher AoA than maximum Cl/Cd and is some
cases is quite close to the stall.

Agreed, except, according to the books, the velocity of minimum power
is ALWAYS less than least drag.