In an isolation transformer, to what is the electrostatic shield winding attached?
I assume channels electrostatic discharge (ESD) away from the
secondary.

From wiki &quot;isolation transformer&quot;: -

The grounded shield prevents capacitive coupling between primary and
secondary windings.

It's not there to stop an ESD event although it will do so in some circumstances providing the shield (the electrostatic shield shown in your picture) is grounded.

It must be connected to something, but what?

Well, the wiki article I found was quite explicit: -

Ground in these circumstances will mean the 0 volt reference point for the circuit you are trying to protect. This also usually means proper earth.

And can the &quot;winding&quot; be just a strap? Or is its isolation also
magnetic in nature, or have a filtering aspect to it?

A winding is used because (a) it is convenient to wind one when constructing the transformer and (b) it won't circulate eddy currents because each turn will be insulated from each other. It's magnetic properties are unrelated to it acting as a shield - only one electrical connection is used with the other end of the winding unterminated or unconnected.