Hi,
Thank you for all the details, it helps me a lot!
There are a few things I noticed, one is, that there is a global transition animation with a custom timing forced on all elements on the page, affecting the scrolling, as well as the positioning. First, I would recommend this custom CSS, to remove this conflicting animation from the search elements:
.asp_w, .asp_w * {
transition-timing-function: unset !important;
transition-duration: unset !important;
}
.asp_r_1_1 {
z-index: 99999999 !important;
}This will also fix the z-index issue with the modal search bar. I have also turned off this option: https://i.imgur.com/S1kgCx5.png
Because the search position is within a fixed container element in both cases, the scrolling effect will do nothing, except a weird scroll down a jump of the results box to correct the mistake.
I also noticed, that on some mobile views, the menu container is wider than the screen, so when the plugin follows the container widh, it is streched from the screen. To resolve that, I recommend setting a fixed container width for mobile screens, maybe 320px or so: https://i.imgur.com/EUheOcv.png
If there is still a noticable issue with scrolling, then maybe turning off the custom scrolling script is the best idea: https://i.imgur.com/ErUSnmV.png
While that script is very robust, some pointer event custom CSS rules or scripts affecting the scroll behavior can conflict with it.
I hope this helps!