Ian, G3SEK wrote:
"---how does the small loss of energy through radiation translate into
dBm or dB/wavelength loss along a transmission line?"

It is the reverse of a beverage antenna, which is a sort of single-wire
transmission line above the earth in its simple configuration. The
Beverage is a horizontal wire sensitive to vertically polarized waves.
It is working with the wave throughout its travel along its length.

The Beverage is vertically polarized because that is the direction of
the electric field between its conductors, the wire and the earth
beneath the wire.

The direction of the electric field in a parallel-wire transmission line
is from wire to wire. The effective radiator length of this polarization
is the line spacing. This is short compared to the length of the
transmission line in nearly all cases. The radiation is not emerging
from the end of the transmission line. It radiates slightly all along
the line as the wave navigates the line, much as the Beverage gathers
energy slightly as the wave sweeps along its length.

Best regards, Richard Harrison, KB5WZI