Why is the screen aspect ratio square ?

The scenes shot in real time seems to have the square.

I think it's to give it a sense of claustrophobia, like the walls are closing in. Or just their idea to distinguish between timelines.

Square was present. Widescreen was past. Until the scene-switch in episode 10 where the past and present meet up (when she’s in the car). Then it was widescreen=present.

The reason for that was the limited version of reality they lived with memory loss.

As the series progresses, we see that not all of the present time is square, and not all of the past is widescreen, as the previous commenter suggests.

It's not square, it's vertical rectangular. That might be not a great difference however my first thought while watching this was that the creators are trying to imitate the smartphone video. This didn't turn out to be true but... that could've been a good thing for creating the 'present feel'. However, that's not correct also.

The series is from 2018.
Heidi and Walter have their 'incidents' on May 15th, 2018.
Later Heidi admits that she was working for 'Homecoming' four years ago.
So technically it's 2022.

Now that could be problematic with her memory being distorted and all but... It really seems like a couple of years have passed because she looks older now (or to put it another way - she looked much younger while working with the program). I have no idea why this was done in such a way, however, it's nothing new seeing like the recent 'Girlfriend Experience' did the same in season 2.

So... widescreen is past, rectangle is near future (2019-2022) but also the graphical depiction of living without certain parts of your memory. And that's how it is through the series: Square/rectangle is present/near future. Widescreen is past.

Until the scene-switch in episode 8 when Heidi and Colin visit the Homecoming facility. She regains her memory and past and present meet up.