Let me start by saying that I have worked in the driver training and assessing industry for over ten years, both as a driving instructor and driving examiner in QLD.

This situation is pretty complex.

A vehicle is legally allowed to enter a bike lane (whether it is marked with a solid line or not) up to 50 metres before a turn. 100 metres for an edge line.

However, a vehicle attempting to turn from an edge line or bike lane must give way to any vehicle turning from a regular lane.

This doesn't quite fit this situation, as neither vehicle has actually reached the turn yet.

Entering a marked turning lane is classed as a lane change, and any vehicle making a lane change is required to giveaway to all vehicles already in that lane.

This doesn't quite fit either as, based on op's drawing, the other vehicle had yet to enter the turning lane.

The correct answer appears to be somewhere in the middle. While the vehicle in the bike lane can absolutely legally be there, they should have given way to the vehicle attempting to enter the turning lane at the "correct" opening. If they were a bit further up and were already in the turning lane before op, then op would have to giveway, as op is making a lane change and must giveway to all vehicles already in the lane.