In the interests of science, I squished a 2 litre PET soda bottle, inverted it, and stuck it mouth down in a sink of water.
The maximum height of water within the bottle was 10cm, but that took a very careful squeeze - compressing the middle of the bottle all round to avoid major creasing. The water level was much lower (5cm) with a flat “across the middle” crease.
So the internal pressure of a squeezed bottle is lower than atmospheric pressure, but not by much. If you have a squeeze and some head space (maybe 1/4 of a bottle), the partial pressure of the CO[sub]2[/sub] will drop and more will come out of solution.
A squeezed bottle with almost no head space will have much less impact on CO[sub]2[/sub] in solution.
Someone really needs to do some maths, comparing a 50% empty bottle with 50% head space, a 50% empty bottle squished with 25% head space, and a 50% empty bottle squished with 5% head space. It’s too late for me here to do that sort of work, but we should have enough info to calculate it out.