I don’t know the answer to that, and I have still to encounter anyone who does.
The best answer you are going to get at the moment is “Spring 2020”.
The original “proof of concept” to refurbish the station while keeping it operational necessitated producing a detailed scheme of works for delivery over 154 weeks.
(
https://www.railengineer.uk/2019/01/31/glasgow-queen-street-station-half-transformed/)
I believe they have managed to adhere to this pretty well (with some minor variations caused by weather, ‘events’ and some changes to the plans). Some phases have been completed ahead of schedule.
We are currently in Week 138; Week ending 22nd March 2020 (the end of week 154) was the original notional date for completion.