Ultra-low Power DC DPDT Switch: Does It Exist?
Voltage levels would be no more than 3.3V, Current less than 150mA
non-continuously, Control voltages also 3.3V and leakage as low as
possible.

What does &quot;as low as possible&quot; mean numerically?

Preferably less than 2-3 μA

Something like this maybe: -

Pick your own from this selector page. Choose (2:1)x2 for device configuration to enable the choices.
Maxim and TI will have similar offerings.