With it rendered in the browser, inspect the elements to see if the jquery plugin is creating additional elements, you would then need to target these from within stimulus and can drill down to them from this.element.
☒ how are you initializing the datepicker? If you have a separate JS file and doing something like a turbolinks:load, make sure that you change those to a turbo:load. Alternatively, I'd recommend making the datepicker a small stimulus controller to initialize it. It will help keep the logic separate and also "just work" when turbo replaces the frame.
I would probably avoid doing window scrolling directly as that could have strange behaviors. You could instead do linking to id tags (anchors) which would scroll the window to the new elements. However, that could also be a bit strange as it would update the history. You would probably need to do something with turbo:before-visit to make sure that you're not creating additional requests back to the server if an anchor tag is present and also check if the user is scrolling to escape the visit entirely.