STM32L1 GPIO pin configuration - Power supply current increase due to pin with open-drain setup
You could use an external pull-up resistor coupled with a BJT, or MOSFET to reduce the junction voltage.
That way, you can enable the pull-up only when the MCU is running.



simulate this circuit &ndash; Schematic created using CircuitLab

Another option is:

2nd attempt was to enable the pull up on the mcu side ( pin is still
output). This had the effect to drive the pin to 2.7V which is not
allowed by the peripheral pin and still there additional current was
observed.

You can make a voltage divider with 2 resistors to reach 1.1V and then use an ADC to read the value.
Even though the voltage is 2.7V, higher than allowed, it might be OK as the current is actually very small as integrated MCU pullup are very high, so the current will be limited to a few uA and shouldn't fry your device. Don't forget to disable the pull-up before putting the MCU to sleep and set the pin as an input.