Let's put the "launching the program and window resizing" effect aside for a moment.

What happens if you move the window from one screen to the other screen and back? The expected behavior would be that the window keeps its size, as far as possible, if ... Assume the screen size is similar (e.g. 21") but the screens have different pixel sizes (effective: different resolutions, dpi). If you set the screen scaling factors in a way that they have similar effective resolutions, then the perceived window size should be "the same" on both monitors. In this case moving the window from one monitor to the other monitor would - at some point in the move - change the internal scaling factor to make the window resize and appear to have (about) the same size.

I don't recall the physical sizes of your monitors. But assume they are the same size (21") and standing side by side. The left (2k = 1920x1080) monitor has scaling factor 100%. The right (4k = 3840x2160) monitor is at scaling factor 200% (which reduces its effective resolution to 1920x1080). Then the window should keep its approximate physical size when you move it from one monitor to the other.

In your setup this might work pretty well if the 2k monitor is @100% and the 4k monitor is @200% or another appropriate scaling factor such that the resolution after applying the scaling is physically the same.

Why am I describing all this? When you move the window from one monitor to the other one there is (should be) a small delay until the window changes its scaling factor (this is done for a "better user experience"). I can't test this, but while you're moving the window from the 2k to the 4k monitor it may first appear bigger (on the 4k monitor) while moving but then - after a short delay - change its size to the "previous" size because the scaling factor is adjusted. This - or something like this - seems to be what you're seeing when you launch the program on the 4k monitor and it gets displayed on the 2k monitor. I'm asking you to test this and report what you see (when moving the window between monitors) because I can't do this myself.

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